Question

What are the zeros of the function y - 2x2 + 7x+3?X = 3O A. *-.*--3O B. x-x-O c. x--3.x-3O D. x=-2.x - 3

Answer 1

EXPLANATION

Given the function:

`y=2x^2+7x+3`
`\mathrm{For\: a\: quadratic\: equation\: of\: the\: form\: }ax^2+bx+c=0\mathrm{\: the\: solutions\: are\: }`
`x_(1,\: 2)=(-b\pm√(b^2-4ac))/(2a)`
`\mathrm{For\: }\quad a=2,\: b=7,\: c=3`
`x_(1,\: 2)=(-7\pm√(7^2-4\cdot\:2\cdot\:3))/(2\cdot\:2)`
`\mathrm{Multiply\: the\: numbers\colon}\: 4\cdot\: 2\cdot\: 3=24`
`=√(7^2-24)`
`7^2=49`
`=√(49-24)`
`\mathrm{Subtract\: the\: numbers\colon}\: 49-24=25`
`=√(25)`
`\mathrm{Factor\: the\: number\colon\: }\: 25=5^2`
`=√(5^2)`
`=5`
`x_(1,\: 2)=(-7\pm\:5)/(2\cdot\:2)`
`Separate\text{ the solutions:}`
`x_1=(-7+5)/(2\cdot\:2),\: x_2=(-7-5)/(2\cdot\:2)`
`\mathrm{The\: solutions\: to\: the\: quadratic\: equation\: are\colon}`
`x=-(1)/(2),\: x=-3`