Question

Hi, I need help please!! Given that x=3 and x=-4 are the solution of the equation x2+ax+b=0, find the value of a and of b. Answer: a=1, b=-12. I don’t know how to get the answer. Please show your workings and explain. If you help me, I will give Brainliest Answer Award to you. The topic is simultaneous equations, algebra. This question is from a Grade 8 workbook.

Answer 1

Answer:

a = 1, b = - 12

Step-by-step explanation:

we know that x = 3 and x = - 4, so (x - 3) and (x + 4) must be the factors of the equation:

(x - 3)(x + 4)

x^2 + - 3x + 4x - 12

x^2 + x - 12

therefore a = 1 and b = - 12

Answer 2

Step-by-step explanation:

firstly substitute x=3 into $x^{2} +ax+b=0$

$3^{2} +3a+b=0$

9+3a+b = 0

          b = -3a-9

secondly substitute x=-4 into $x^{2} +ax+b=0$

$(-4)^{2} +(-4)a+b=0$

16-4a+b = 0

          b = 4a-16

combine the equations above,

-3a-9 = b = 4a-16

so -3a-9 = 4a-16

     7a = 7

       a = 1

then substitute a = 1 into b = 4a-16 or b = -3a-9 (both are ok)

b = 4(1)-16 = -12     or        b = -3(1)-9 = -12