Question

What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?

Answer 1

`x=-2-\sqrt{(11)/(2)}\ \text{and}\ x=-2+\sqrt{(11)/(2)}`

Explanation:

My favorite way to go at this is to look at a graph. It shows the vertex at (-2, -11). Since the leading coefficient is 2, this means the roots are ...

`-2\pm\sqrt{(11)/(2)}`

where the 2 in the denominator of the radical is the leading coefficient.

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You can also use other clues:

• the axis of symmetry is -b/(2a) = -8/(2(2)) = -2, so answer choices C and D don't work
• the single change in sign in the coefficients (+ + -) tells you there is one positive real root, so answer choice B doesn't work.

The first answer choice is the only one with values symmetrical about -2 and one of them positive.

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You may be expected to use the quadratic formula:

`x=(-b\pm√(b^-4ac))/(2a)=(-8\pm√(8^2-4(2)(-3)))/(2(2))\\\\=(-8)/(4)\pm(√(88))/(4)=-2\pm\sqrt{(11)/(2)}`