Question

Which statement about the following equation is true?

2x2 – 9x + 2 = –1
The discriminant is less than 0, so there are two real roots.
The discriminant is less than 0, so there are two complex roots.
The discriminant is greater than 0, so there are two real roots.
The discriminant is greater than 0, so there are two complex roots.

Answer 1

Answer:

The discriminant is greater than 0, so there are two real roots.

Step-by-step explanation:

$\boxed{\begin{minipage}{6.2 cm}\underline{Discriminant}\\\\ b^2-4ac \quad when ax^2+bx+c=0 \\\\If b^2-4ac > 0 \implies two real roots\\If b^2-4ac=0 \implies one real root\\If b^2-4ac < 0 \implies no real roots\\\end{minipage}}$

Given equation:

$2x^2-9x+2=-1$

Add 1 to both sides of the equation so that the equation equals zero:

$\implies 2x^2-9x+2+1=-1+1$

$\implies 2x^2-9x+3=0$

Compare the equation with ax²+bx+c=0:

• a = 2
• b = -9
• c = 3

Substitute the values of a, b and c into the discriminant formula and solve:

$\begin{aligned}\implies b^2-4ac&=(-9)^2-4(2)(3)\\&=81-4(2)(3)\\&=81-8(3)\\&=81-24\\&=57\end{aligned}$

As 57 > 0, the discriminant is greater than zero, so there are two real roots.