Question

If a and ß are the zeroes of the polynomial kx2 + 3x + 2, such that a2 + B2. aß = find
25
the value of k.​

Answer 1

Answer:

Question:

If α and β are the zeros of quadratic polynomial f(x)=kx² +4x+4 such that α² +β² =24, find the value of k.

gívєn

polynomial- kx²+4x+4

a²+ß²= 24

To Find

value of k.

solution

polynomial- kx²+4x+4

$\bold{sum \: of \: zeros = \frac{ - b}{a} }$

➠ a+ß= -4/k

$\bold{product \: of \:zeros = \frac{c}{a} }$

➠ a x ß= 4/k

➠identity-

(a+ß)²= a²+ß²+2aß

put the value in the identity:

➠(-4/k)²= 24+ 2 x 4/k

➠16/k²= 24+ 8/k

by solving this further we get a quadratic equation-

➠24k²+ 8k- 16= 0

➠3k²+k- 2= 0

By middle term split

➠3k²+3k-2k-2=0

➠3k(k+1) -2(k+1)=0

➠(3k-2) (k+1)= 0

➠k= 2/3 , -1

▪️hence value of k is 2/3 , -1.