Home
Class 12
MATHS
If x^2+(a-b)x=(1-a-b)=0. w h e r ea ,b i...

If `x^2+(a-b)x=(1-a-b)=0. w h e r ea ,b in R ,` then find the values of `a` for which equation has unequal and real roots

Text Solution

Verified by Experts

The correct Answer is:
`a gt1`
Given, `x^(2)+(a-b)x+(1-a-b)=0` has real and unequal roots.
`implies D gt0`
`implies(a-b)^(2)-4(1)(1-a-b)gt0`
`implies a^(2)+b^(2)-2ab-4+4a+4bgt0`
Now, to find the values of 'a' for which equation has unequal real roots for all values of b.
i.e. Above equation is true for all b.
`orb^(2)+b(4-2a)+(a^(2)+4a-4)gt0, ` is true for all b.
`therefore` Discriminant, `Dlt0`
`implies(4-2a)^(2)-4(a^(2)+4a-4)lt0`
`implies16-16a+4a^(2)-4a^(2)-16a+16lt0`
`implies-32a +32 lt 0 impliesa gt1`
Promotional Banner

Similar Questions

Explore conceptually related problems

If x^2+(a-b)x+(1-a-b)=0. w h e r ea ,b in R , then find the values of a for which equation has unequal real roots for all values of bdot

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,t h e n

If a x^2+b x+6=0 does not have distinct real roots, then find the least value of 3a+bdot

If a ,b ,c in R , then find the number of real roots of the equation Delta =|[x, c,-b],[-c, x, a], [b,-a,x]|=0

If a and b are roots of equation x^(2)-PX+Q=0 , find the value of 1/a+1/b .

If |x^n x^(n+2)x^(2n)1x^a a x^(n+5)x^(a+6)x^(2n+5)|=0,AAx in R ,w h e r en in N , then value of a is n b. n-1 c. n+1 d. none of these

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.