Question

If zeros of x^2 - kx +6 are in the ratio 3:2 find k

Answer 1

Answer:

The answer will be -5.

Step-by-step explanation:

Ratio of the zeros is;

= 3:2

Let the first zero be 3y. Thus another will be 2y.

Now, we know that;

α + β= -b/a;

and, αβ = c/a;

here, α and β are the zeroes of the polynomial.

Hence, if α = 3y then β = 2y.

{Remember, zeroes and roots are same terms in quadratic equation.}

Thus, αβ = 6/1. (c=6 and a= 1)

(3y)(2y) = 6

6y^2 = 6

y^2 = 1

y = 1. (i)

Now, α + β = c/a

( 3y) + (2y) = -k/1. ( since, b= k and c=1)

(3)(1) + (2)(1) = -k. (y = 1, from eq. (i))

3 + 2 = -k

-k = 5

k = -5.

That's all.