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8_murik_8 [283]
2 years ago
11

What are the zeros of the quadratic function f(x) = 8x2 – 16x – 15?

Mathematics
2 answers:
marusya05 [52]2 years ago
4 0

8x^2 - 16x - 15 = 0

x = [ -(-16) +/- sqrt((-16)^2 - 4*8*-15) / ] 2*8

= 2.696, -0.696

denis23 [38]2 years ago
3 0

Answer:

The zeroes of the given polynomial f(x) are

x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}

Step-by-step explanation:

Given : Quadratic function f(x)=8x^2-16x-15

To find : What are the zeros of the quadratic function?

Solution :

Using quadratic formula of the general equation ax^2+bx+c=0 to get the roots is x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

Comparing the given quadratic equation,

a = 8, b = -16  and  c = - 15.

Substitute the value in the formula,

x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-(-16)\pm\sqrt{(-16)^2-4\times 8\times (-15)}}{2\times 8}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{256+480}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm\sqrt{786}}{16}\\\\\\\Rightarrow x=\dfrac{16\pm4\sqrt{46}}{16}\\\\\\\Rightarrow x=\dfrac{4\pm\sqrt{46}}{4}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{46}{16}}\\\\\\\Rightarrow x=1\pm\sqrt{\dfrac{23}{8}}\\\\\\\Rightarrow x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}.

Therefore, The zeroes of the given polynomial f(x) are

x=1-\sqrt{\dfrac{23}{8}},~~~x=1+\sqrt{\dfrac{23}{8}}

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