Consider a quadratic equation $ax^2 + bx + c = 0,$ where $2a + 3b + 6c = 0$ and let $g(x) = a\frac{{{x^3}}}{3} + b\frac{{{x^2}}}{2} + cx.$
Statement $1:$ The quadratic equation has at least one root in the interval $(0, 1).$
Statement $2:$ The Rolle's theorem is applicable to function $g(x)$ on the interval $[0, 1 ].$
Consider a quadratic equation $ax^2 + bx + c = 0,$ where $2a + 3b + 6c = 0$ and let $g(x) = a\frac{{{x^3}}}{3} + b\frac{{{x^2}}}{2} + cx.$
Statement $1:$ The quadratic equation has at least one root in the interval $(0, 1).$
Statement $2:$ The Rolle's theorem is applicable to function $g(x)$ on the interval $[0, 1 ].$
- [AIEEE 2012]
- A
Statement $1$ is false, Statement $2$ is true.
- B
Statement $1$ is true, Statement $2$ is false.
- C
Statement $1$ is true, Statement $2$ is true,Statement $2$ is not a correct explanation for Statement $1.$
- D
Statement $1$ is true, Statement $2$ is true, Statement $2$ is a correct explanation for Statement $1.$
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- [JEE MAIN 2015]
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