If the roots of the equation 6x^2 - 7x + k = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For the roots of a quadratic equation $ax^2 + bx + c = 0$ to be rational,the discriminant $D = b^2 - 4ac$ must be a perfect square.Here,$a = 6$,$b

Vedclass · Accepted Answer

$1, 2$

Vedclass · Answer

(B) For the roots of a quadratic equation $ax^2 + bx + c = 0$ to be rational,the discriminant $D = b^2 - 4ac$ must be a perfect square.Here,$a = 6$,$b = -7$,and $c = k$.$D = (-7)^2 - 4(6)(k) = 49 - 24k$.For $D$ to be a perfect square,we test values of $k$:If $k = 1$,$D = 49 - 24(1) = 25 = 5^2$ (a perfect square).If $k = 2$,$D = 49 - 24(2) = 49 - 48 = 1 = 1^2$ (a perfect square).Thus,the values of $k$ for which the roots are rational are $1$ and $2$.

If the roots of the equation $6x^2 - 7x + k = 0$ are rational,then $k = .......$

Similar Questions

If ${b_1}{b_2} = 2({c_1} + {c_2})$,then at least one of the equations ${x^2} + {b_1}x + {c_1} = 0$ and ${x^2} + {b_2}x + {c_2} = 0$ has

The real root of the equation $x^{3}-6x+9=0$ is

The number which exceeds its positive square root by $12$ is

Given $f(x) = ax^2 + bx + c$,$g(x) = a_1x^2 + b_1x + c_1$,and $p(x) = f(x) - g(x)$. If $p(x) = 0$ only for $x = -1$ and $p(-2) = 2$,what is the value of $p(2)$? Assume $a \neq a_1 \neq 0$.

Let $f(x) = ax^{2} + bx + c$ be such that $f(1) = 3$,$f(-2) = \lambda$,and $f(3) = 4$. If $f(0) + f(1) + f(-2) + f(3) = 14$,then $\lambda$ is equal to...

Vedclass Test Series

Exam Paper Generator

Online Exam Module