Answer:
b = 3
c = -70
Step-by-step explanation:
[tex]\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}}[/tex]
If a quadratic equation [tex]ax^2+bx+c=0[/tex] has -10 and 7 as its solutions, then applying the zero product property in reverse gives its factors:
[tex]x=-10 \implies (x+10)=0[/tex]
[tex]x=7 \implies (x-7)=0[/tex]
Therefore,
[tex]\implies a(x+10)(x-7)=0[/tex]
As a = 1, then:
[tex]\implies (x+10)(x-7)=0[/tex]
Expand the brackets:
[tex]\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}[/tex]
Compare with [tex]ax^2+bx+c=0[/tex] :
