Question

A quadratic equation ax²+bx+c=0 has -10 and 7 as solutions. Find the values of b and c if the value of a is 1. (Hint: Use the zero-factor property in reverse.)

Question 10, 1.4.95 >

Answer 1

b = 3

c = -70

Explanation:

`\boxed{\begin{minipage}{8.5 cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}`

If a quadratic equation
`ax^2+bx+c=0` has -10 and 7 as its solutions, then applying the zero product property in reverse gives its factors:

`x=-10 \implies (x+10)=0`

`x=7 \implies (x-7)=0`

Therefore,

`\implies a(x+10)(x-7)=0`

As a = 1, then:

`\implies (x+10)(x-7)=0`

Expand the brackets:

`\begin{aligned}\implies (x+10)(x-7)&=0\\x(x-7)+10(x-7)&=0\\x^2-7x+10x-70&=0\\x^2+3x-70&=0\end{aligned}`

Compare with
`ax^2+bx+c=0` :

• a = 1
• b = 3
• c = -70