Question

The difference between the roots of the quadratic equation x^2−14x+q=0 is 6. Find q.

someone pls helpppp

Answer 1

The value of q is 40

Explanation:

Let one root = a

other root = b

x²-14x+q = (x-a)(x-b)

= x²-bx-ax+ab

= x²-(a+b)x+ab

Comparing the

coefficient

a + b = 14 ----(1)

ab = q -----(2)

a - b = 6 ------(3)

(1)-(3)

2b = 8

b = 4

sub b=4 into(1)

a + 4 = 14

a = 10

sub a=10,b=4 into(2)

ab = q

q = 10×4

= 40

Answer 2

q=-1128/169

Explanation:

x²n-14x+q=0 here a=1, b= -14, c=q

let the roots of the equation beα and β

then the sum of the roots= S= α+β= -b/a=-(-14)/1=14

α+β=14 ⇒β=14-α--------(i)

product of the roots=P= αβ= c/a= q/1=q------(ii)

since α-β=6--------(given)----(iiI)

put the values of β from equation i to equation iii

α-14α=6

-13α=6

α=-6/13

put the values of α and β in eq. (ii)

αβ=q=(-6/13)(14-(-6/13)

q=(-6/13)(182+6/13)

q=(-6/13)188/13

q=-1128/169