Question

If x=2 and x=3 are roots of the quadratic equation ax2+7x+b=0, find the values of a and b.

Answer 1

we know if roots are given
then sum of roots =-coefficient of x/ coefficient of x^2
2+3=-7/a
a=-7/5
also multiple of roots =constant/coefficient of x^2
2x3=b/a
b=6a=6(-7/5)=-42/5
b=-42/5

Answer 2

Answer:

The values are a = -17/5 & b = -2/5

Step-by-step explanation:

According to the given problem;

f(x) = a*x²+7*x+b

At x = 2;

f(2) = a(2)²+7(2)+b=0

4*a+14+b= 0  

4*a + b = -14 ------- (A)

Now again the given function;

f(x) = a*x²+7*x+b

At x = 3;

f(3)= a(3)²+7(3)+b= 0

9*a + 21 + b = 0

9*a + b = -21 ---------(B)

Solving (A) and (B) simultaneously;

a = -17/5

b = -2/5