Question

Find the positive value of k for which the given quadratic equation has real and equal roots

Answer 1

Hey there,

If you don't want to incorporate your prior knowledge to the problem, the quadratic equation has equal roots when the discriminant is equal to zero. (k−1)²+ 4(1) (1+2k) = k² + 6k + 5 = (k+1) (k+5) = 0 ⟺ k∈ {−5,−1}

Hope this helps!

Answer 2

if the equaion x2+kx+64=0 has real roots, then D>=0k2-256>=0 => k2>=256 => k2>=(16)2 => k>=16.- (1)if the equation x2-8x+k=0 has real roots.then D>=0 => 64-4k>=0 => 4k<=64 => k<=16 - (2)from (1) and (2) we get k=16