Question

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

Answer 1

hope it helps.........

Answer 2

$heya \\ \\ \\ \alpha + \beta = - 4 \div k \\ \\ \\ and \\ \\ \\ \\ \alpha \beta = 4 \div k \\ \\ \\ \\ \alpha {}^{2} + \beta {}^{2} = ( \alpha + \beta ) {}^{2} - 2 \alpha \beta = 24\\ \\ \\ ( \alpha + \beta ) {}^{2} - 2 \alpha \beta = 24 \\ \\ \\ (16 \div k {}^{2} ) - 2(4 \div k) = 24 \\ \\ \\ 16k - 8k {}^{2} = 24k {}^{3} \\ \\ \\ \\ 24k { }^{3} + 8k {}^{2} - 16k = 0 \\ \\ \\ k = 0 \: \: \: or \: \: \: \: \: 3k {}^{2} + k {}^{2} - 2 = 0 \\ \\ \\ \\ 3k {}^{2} + 3k - 2k - 2 = 0 \\ \\ \\ k = - 1 \: \: \: \: or \: \: \: \: k = 2 \div 3$