Question

In solving a quadratic equation, Mahendar made a mistake in taking the product of the roots and got roots of equation as 5 and 1. Niranjan made a mistake in taking the sum of roots and got roots of equation as 8 and 1. What are the actual roots of the equation?

Answer 1

Answer:

5,4

online test 2023 MOT ,Q.75

Step-by-step explanation:

Answer 2

The actual roots of the equation are 2 and 4

Step-by-step explanation:

Let the actual roots of the equation are $\alpha$ and $\beta$

Quadratic equation whose roots are 5 and 1 has correct sum of roots

Thus,

$\alpha+\beta=5+1=6$

Quadratic equation whose roots are 8 and 1 has correct product of roots

Thus,

$\alpha\beta=8\times 1$

$\implies \beta=\frac{8}{\alpha}$

Therefore,

$\alpha+\frac{8}{\alpha}=6$

$\implies \alpha^2-6\alpha+8=0$

$\implies \alpha^2-4\alpha-2\alpha+8=0$

$\implies \alpha(\alpha-4)-2(\alpha-4)=0$

$\implies (\alpha-4)(\alpha-2)=0$

$\implies \alpha=4,2$

If we take $\alpha=4$

Then $\beta=2$

If we take $\alpha=2$

Then $\beta=4$

Therefore, the actual roots of the equation are 2 and 4

Hope this answer is helpful.

Know More:

Q: Two candidates attempt to solve a quadratic equation of the form x^2+px+q=0. One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a wrong value of q and finds the roots to be 2 and – 9. Find the correct roots of the equation :

Click Here: https://brainly.in/question/4172456

Q: In solving a quadratic equation, Samrat made a mistake in noting the constant term and found the roots to be 8 and 2.sarbojeet made a mistake in noting the coefficient of X and found the roots to be-9 and -1.what are the correct roots of the equation?​

Click Here: https://brainly.in/question/12771799