Question

If 'o' and 'Bare the roots of the equation +7x + 12 = 0, the equation whose roots are
+ B) and (a - b) is
+ 50 X + 49 50
b) x 50 X + 49 - 0
ca 50 49 -
​

Answer 1

Step-by-step explanation:

a and b are the roots of x^2+7x+12=0

By middle term factorization,

x^2+3x+4x+12=0

x(x+3)+4(x+3)=0

(x+3)(x+4)=0

x+3=0, x+4=0

x=-3, x=-4

So a=-3 and b=-4

Given that, the roots of an equation is (a+b) ^2 and (a-b) ^2

So, (a+b) ^2=(-3-4)^2=-7^2=49

(a-b)^2=(-3-(-4))^2=(-3+4)^2=1

We know that, quadratic equation is

x^2-(a+b)x+ab=0

x^2-(49+1)x+49(1)=0

x^2-50x+49=0

So, the quadratic equation is x^2-50x+49=0