Question

A quadratic equation of the form 0 = ax2 + bx + c has a discriminant value of –16. How many real number solutions does the equation have?

Answer 1

`\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{a}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ \stackrel{-16}{negative}&\textit{no solution}~~\checkmark \end{cases}`

Answer 2

A quadratic equation of the form 0 = ax² + bx + c with a discriminant value of –16 has no real solution

Explanation:

A quadratic equation ax²+bx+c=0 with discriminant D=b²-4ac has

2 unequal real solutions if D is positive i.e. D>0

2 equal real roots if D=0

no real root if D is negative i.e. D<0

Here, we are given value of D= -16 which is less than zero

Hence, a quadratic equation of the form 0 = ax² + bx + c with a discriminant value of –16 has no real solution