Question

a quadratic equation has a discriminant of 12. which could be the equation?
0 = -x² + 8x + 2
0 = 2x² + 6x + 3
0 = -x² + 4x + 1
0 = 4x² + 2x + 1

Explanation:

Step1: Recall discriminant formula

For quadratic $ax^2+bx+c=0$, discriminant $\Delta = b^2-4ac$.

Step2: Calculate for first equation

$0=-x^2+8x+2$, so $a=-1,b=8,c=2$
$\Delta = 8^2 - 4(-1)(2) = 64 + 8 = 72$

Step3: Calculate for second equation

$0=-x^2+4x+1$, so $a=-1,b=4,c=1$
$\Delta = 4^2 - 4(-1)(1) = 16 + 4 = 20$

Step4: Calculate for third equation

$0=2x^2+6x+3$, so $a=2,b=6,c=3$
$\Delta = 6^2 - 4(2)(3) = 36 - 24 = 12$

Step5: Calculate for fourth equation

$0=4x^2+2x+1$, so $a=4,b=2,c=1$
$\Delta = 2^2 - 4(4)(1) = 4 - 16 = -12$

Answer:

$0=2x^2+6x+3$