Question

2x2 – 9x + 2 = –1

Answer 1

Answer:

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

Step-by-step explanation:

Discriminant

$b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0$

$\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}$

$\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}$

$\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}$

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

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

$\implies a=2, b=-9, c=3$

$\begin{aligned}b^2-4ac &=(-9)^2-4(2)(3)\\& =81-24\\&=57 > 0\implies \textsf{two real roots}\end{aligned}$