Question

if alpha and beta are zeros of quadratic polynomial f(x)= kx^2+4x-4, such that alpha^2+beta^2=24 find k​

Answer 1

Answer:

Step-by-step explanation:

Sum of roots of a quadratic equation= -coefficient of x÷coefficient of x²

Product of roots of the quadratic equation= constant÷coefficient of x²

sum of roots= alpha +beta= -4÷k

product of roots=-4÷k

alpha² + beta²= (alpha+beta)²- 2×alpha×beta

Given: alpha²+ beta²=24;

24= (16÷k²)+(8÷k)

24k²=16+8k

3k²=2+k

3k²-k-2=0

3k²-3k+2k-2=0

3k(k-1)+2(k-1)=0

k=1 or k=-2÷3

Thus k can take two values as mentioned above.