a quadratic equation has a discriminant of 12. which could be the equation?\n0 = -x² + 8x + 2\n0 = 2x² + 6x…

Explanation:

Step1: Recall discriminant formula

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

Step2: Check option A

For $y=-x^{2}+8x + 2$, where $a=-1$, $b = 8$, $c = 2$. Then $\Delta=(8)^{2}-4\times(-1)\times2=64 + 8=72$.

Step3: Check option B

For $y = 2x^{2}+6x+3$, where $a = 2$, $b = 6$, $c = 3$. Then $\Delta=(6)^{2}-4\times2\times3=36-24 = 12$.

Step4: Check option C

For $y=-x^{2}+4x + 1$, where $a=-1$, $b = 4$, $c = 1$. Then $\Delta=(4)^{2}-4\times(-1)\times1=16 + 4=20$.

Step5: Check option D

For $y = 4x^{2}+2x+1$, where $a = 4$, $b = 2$, $c = 1$. Then $\Delta=(2)^{2}-4\times4\times1=4 - 16=-12$.

Answer:

B. $0 = 2x^{2}+6x + 3$