Question

If one root of the equation ax² – 7x + 12 = 0 is 3, then find the value of ‘a’.​

Answer 1

Answer:

The given quadratic equation is kx2 - 7x + 12 = 0.

Let α and β be the roots of the given equation.

Comparing the given equation with the standard equation,

ax2+ bx+ c =0, we have,

a = k, b =- 7 and c 12.

Thus,α+β=-ba=--7k

andαβ=ca=12k

Since one of the roots is 3, we have,

3+β=7kand3β=12k

3+β=7kandβ=4k

Substituting the value of β=4k

3+4k=7k

3k+4k=7k

3k+4=7

3k=7-4

3k=3

k=1

Step-by-step explanation:

Hi !!

Hope it helps you !!

Answer 2

Answer:

a=1

Step-by-step explanation:

as 3 is one root of the given equation

just substitiute 3 in place of x and equate it to 0

a(3)²- 7(3) + 12= 0

9a- 21 +12=0

9a= 9

a=1