Home
Class 12
MATHS
If b gt a, then the equation (x-a)(x-b)-...

If `b gt a`, then the equation `(x-a)(x-b)-1=0`, has

A

both roots in `(a,b)`

B

both roots in`(-oo, a)`

C

both roots in `(b,+oo)`

D

one root in `(-oo,a)` and the other in in `(b,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D

From graph, it is clear that one of the roots of `(x-a)(x-b)-1=0` line in `(-oo,a)` and other lies in `(b,oo).`
Promotional Banner

Similar Questions

Explore conceptually related problems

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

Let a, b and c be real numbers such that 4a + 2b + c = 0 and ab gt 0. Then the equation ax^(2) + bx + c = 0 has

If a

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imaginary roots, then (a+b+1) is a. positive b. negative c. zero d. Dependent on the sign of b

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q(b) (1)/(alpha)+(1)/(beta)

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot