Question

The zero of the polynomial x^2 - x - 110 are (a) 11 , -10 (b) -11 , 10 (c) -11 , -10 (d) 11 ,10​

Answer 1

Step-by-step explanation:

Given equation x

2

−10cx−11d=0 with a,b and x

2

−10ax−11b=0 with c,d

a+b=10c and c+d=10a

⇒(a−c)+(b−d)=10(c−a)

⇒(b−d)=11(c−a) ...(i)

Since, c is the root of x

2

−10ax−11b=0

⇒c

2

−10ac−11b=0 ...(ii)

Similarly, a is the root of x

2

−10cx−11d=0

⇒a

2

−10ca−11d=0 ...(iii)

On subtracting equation (iii) from (ii), we get

(c

2

−a

2

)=11(b−d) ...(iv)

∴(c+a)(c−a)=11×11(c−a) [from (i)]

⇒c+a=121

∴a+b+c+d=10c+10a

=10(c+a)=1210