Find the roots of f(x)=x^2+10x−96

Mathematics

1 answer:

a_sh-v [17]3 years ago

6 0

Answer:

x = -16 or x = 6

Step-by-step explanation:

To find the roots of a polynomial function, set the polynomial equal to zero and solve for x.

x² + 10x - 96 = 0

We need to factor the left side. The left side is a quadratic polynomial whose first coefficient is 1. We need two numbers whose product is -96 and whose sum is 10. The numbers are 16 and -6.

(x + 16)(x - 6) = 0

If a product of two factors equals zero, then one factor or the other or both must equal zero.

x + 16 = 0 or x - 6 = 0

x = -16 or x = 6

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With given information, we have $\frac{TR}{TQ} = \frac{TS}{TP}$ , so $\frac{5}{13} = \frac{3w}{3w+3}$ , which gives us $w=\frac{5}{8}$ . Meanwhile, we have $\frac{TR}{TQ}=\frac{RS}{QP}$ , so $\frac{5}{13}=\frac{10}{2v+5}$ , which gives us $v = \frac{21}{2}$ .