Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.


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 >

Sagot :

semsee45

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] :

  • a = 1
  • b = 3
  • c = -70
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.