Question

lf the sum of roots of quadratic polynomial ky^2+2y-3k is equal to twice their products find the value of k ​

Answer 1

Heya!

GIVEN QUADRATIC POLYNOMIAL IS

ky² + 2y - 3k

This Quadratic polynomial has two roots let those two roots be a and b

a + b = -2/k

And

a×b = -3k/k = -3

ACCORDING TO THE GIVEN QUESTION

( a + b ) = 2 ( a×b)

( -2/k ) = 2 ( -3 )

k = 1/3

Answer 2

Solution:-

Given Quadratic Polynomial Equation :-

• ky² + 2y - 3k = 0

A.T.Q.

Sum of Roots = 2 × Product of Roots.

=) α + β = 2 αβ __________(1)

Now, Finding α + β.

=) α + β = -b/a

=) α + β = -2/k

Now, Finding αβ.

=) αβ = c/a

=) αβ = -3k/k

=) αβ = -3

Substituting the values of αβ and α + β in Equation (1).

=) α + β = 2 αβ

=) -2/k = -2 ( 3 )

=) 2/k = 2 (3)

=) 1/k = 3

=) k = 1/3.