Questions
If are real numbers such that , then the quadratic equation has
a
At least one root in [0, 1]
b
At least one root in [1, 2]
c
At least one root in [-1, 0]
d
None of these
detailed solution
Correct option is A
Let f1(x) denotes the quadratic expression f1(x)=3ax2+2bx+c, whose antiderivative be denoted by f(x)=ax3+bx2+cxNow f(x) being a polynomial in R, f(x) is continuous and differentiable on R. To apply Rolle's theorem.We observe that f(0)=0 and f(1)=a+b+c=0, by hypothesis. So there must exist at least one value of x, say x=α∈(0,1) such thatf1(α)=0⇔3aα2+2bα+c=0That is, f1(x)=3ax2+2bx+c=0 has at least one root in [0, 1]Talk to our academic expert!
Similar Questions
In which of the following function is rolle’s theorem applicable?
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