how many real number soulutions does this equations have? 0=4x^2+7x-8

Question

i need help really bad

Answer 1

Without solving, it's clear that there are two real roots because the discriminant will be positive due to -8 as the constant (b^2-4ac is a positive number because c<0).

4x^2+7x-8=0; x^2+7x/4=2; x^2+7x/4+49/64=2+49/64; (x+7/8)^2=(128+49)/64=177/64.

Taking square roots of each side: x+7/8=+sqrt(177)/8, so there are two real roots.

sqrt(177)=13.3041 approx, so x=-0.875+1.66302=0.78802 or -2.53802