Question

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of 0. How many real number solutions does the equation have?

Answer 1

It has one solution. when discriminant=0, tangent to the curve( means touches at one point ) hence one solution.

Answer 2

we know that

the formula to solve a quadratic equation of the form $ax^{2}+bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}$

The discriminant is equal to

$(b^{2}-4ac)$

If the discriminant is equal to zero

then

$(b^{2}-4ac)=0$

substitute in the formula

$x=\frac{-b(+/-)\sqrt{0}}{2a}$

$x=-\frac{b}{2a}$-------> only one real number solution

therefore

the answer is

the number of solutions is equal to $1$