These solutions for Quadratic Equations are extremely popular among Class 10 students for Math Quadratic Equations Solutions come handy for quickly completing your homework and preparing for exams. Therefore, or. Hence, or. We have been given. Find the roots of the following quadratic equations if they exist by the method of completing the square. Therefore the roots of the equation are and. We have to find the roots of given quadratic equation by the method of completing the square.
We have,. We should make the coefficient of unity. Now add square of half of coefficient of on both the sides,. So the required solution of ,.
Since RHS is a negative number, therefore the roots of the equation do not exist as the square of a number cannot be negative. Now divide throughout by. We get,. Now we also know that for an equation , the discriminant is given by the following equation:. Now, according to the equation given to us, we have, , and.
Therefore, the discriminant of the equation is. Since, in order for a quadratic equation to have real roots,. Here we find that the equation satisfies this condition, hence it has real roots. Therefore, the roots of the equation are and. Here we find that the equation does not satisfies this condition, hence it does not have real roots. Here we find that the equation satisfies this condition, hence it has real and equal roots. Therefore, the roots of the equation are real and equal and its value is.
Therefore, the value of ii We have been given,. Therefore, the value of iii We have been given,. Therefore, the value of iv We have been given,. Which of the following are quadratic equations? We are given the following algebraic expressions and are asked to find out which one is quadratic. Now, the above equation clearly represents a quadratic equation of the form , where , and. Now, the above equation clearly does not represent a quadratic equation of the form , because is a polynomial of degree 3.
Now, the above equation clearly does not represent a quadratic equation of the form , because contains a term , where is not an integer.
Now, as we can see the above equation clearly does not represent a quadratic equation of the form , because contains an extra term , where is not an integer. Now as we can see, the above equation clearly represents a quadratic equation of the form , where , and. Now as we can see, the above equation clearly does not represent a quadratic equation of the form , because is a polynomial having a degree of 4 which is never present in a quadratic polynomial.
Now as we can see, the above equation clearly does not represent a quadratic equation of the form , Byjus Maths Class 8 Textbook 5 Pdf because is a linear equation. Now as we can see, the above equation clearly does not represent a quadratic equation of the form , because is a polynomial having a degree of 3 which is never present in a quadratic polynomial. Now as we can see, the above equation clearly does not represent a quadratic equation of the form , because is a linear equation which does not have a term in it.
We are given the following quadratic equations and we are asked to find whether the given values are solutions or not. Now if is a solution of the equation then it should satisfy the equation. So, substituting in the equation we get. Hence, is a solution of the given quadratic equation. Also, if is a solution of the equation then it should satisfy the equation. So, substituting in the equation, we get. Hence is not a solution of the quadratic equation. Therefore, from the above results we find out that is a solution and is not a solution of the given quadratic equation.
Hence is not a solution of the given quadratic equation. Therefore, from the above results we find out that both and are not a solution of the given quadratic equation.
Hence is a solution of the quadratic equation. Therefore, from the above results we find out that and are the solutions of the given quadratic equation. Hence, is not a solution of the quadratic equation.
Therefore, from the above results we find out that both and are not the solutions of the given quadratic equation. Hence is a solution of the given quadratic equation. Therefore, from the above results we find out that both and are solutions of the quadratic equation.
Therefore, from the above results we find out that is a solution but is not a solution of the given quadratic equation. Therefore, from the above results we find out that is not a solution and is a solution of the given quadratic equation. Now, as we know that is a solution of the quadratic equation, hence it should satisfy the equation.
Therefore substituting in the above equation gives us,. Hence, the value of. Hence the value of. As we know that. Putting the value of. Therefore, root of the given equation are. The given equation will have real and equal roots, if. Therefore, the value of. The given equation will have real roots, if.
The given equation will have real and distinct roots, if. The given quadric equation is , and roots are real and equal. The given quadric equation is , and roots are real. Also, find the roots. Therefore, the value of k is 0 or 1. Also, find these roots. Therefore, the value of p is 4 or - 4 7. Then, it satisfies the given equation.
Therefore, the value of k is 7 4. Therefore, the value of b is 9. Hence, find the roots of the equation. Disclaimer: There is a misprinting in the given question. In the question ' q ' is printed instead of 9. Determine the set of values of k for which the following quadratic equation have real roots: i ii iii iv.
Since left hand side is always positive. Then prove that. Let be the discriminants of equation 1 and 2 respectively,. Both the given equation will have real roots, if. The quadric equation is. Since , P and q are real and , therefore, the value of. The given quadric equation is , and roots are equal. Then prove that either or. Thus, the value of. So the solutions are real. Therefore, the roots of the given equation are real and but they are equal only when,.
Now given that are real number and as well as from equations 3 and 4 we get. The given equation , has equal roots. Now, if is a root of the above quadratic equation, then it should satisfy the whole. So substituting in the above equation, we have,. Now since, we can see from above that left hand side and right hand side are not equal. Therefore is not the solution of the given quadratic equation.
Now, if is a root of the equation, then it should satisfy the equation completely. Therefore we substitute in the above equation. Also, if is a root of the equation, then it should satisfy the equation completely.
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