Question

If the roots of the equation (x + 1) (x + 9) + 8 = 0 are a and b, then the roots of the equation (x + a) (x + b) -8 = 0 are

(1) 1 and 9 (2) -4 and -6 (3) 4 and 6 (4) Cannot be determined

Answer 1

Solution :-

We will here use the properties of roots of a quadratic equation of the form cx^2+dx+e=0.

If p and q are the two roots of the above equation, then

p+q= - (d/c)

and pq=(e/c)

Now , Expanding the first equation (x+1)(x+9)+8=0 we have : x^2+10x+17=0

Since ‘a’ and ‘b’ are the roots of the above equation we must have:

a+b= - (10/1)= -10

and a.b=(17/1)=17

Now expanding the second equation ( x+a) (x+b) - 8 = 0 So , we get:

x^2+(a+b)x+a.b-8=0

=> x^2+(-10)x+17–8=0

=>x^2–10x+9=0

=>x^2–9x-x+9=0

=>x(x-9)-(x-9)=0

=>(x-1)(x-9)=0

=>x=1 or x=9

Hence the two roots of the equation are 1 and 9. So A option is correct answer.