Question

the quadratic equation for which the sum of roots is 7 and sum of squares of the roots is 25


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Answer 1

Answer:

Then the quadratic equation will be x^2-(a+b)x+ab

Given a+b=7

a^2+b^2=25

So 2ab=(a+b)^2-a^2-b^2

=7^2-25=49-25=24

ab=24/2=12

So the required equation is

x^2-7x+12

Step-by-step explanation:

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Answer 2

SOLUTION:-

Let α and β be the two roots of Quadratic equation.

α + β = 7

α² + β²= 25

now,

α² + β² = (α + β)² - 2αβ

25 = (7)² - 2αβ

25 = 49 - 2αβ

25 - 49 = - 2αβ

- 24 = -2αβ

αβ = 24/2

αβ = 12

now,

Quadratic equation

=> x² - (α + β)x + αβ = 0

x² - (7)x + 12 = 0

x² - 7x + 12 = 0

The quadratic equation is x² - 7x + 12 = 0