A student,while solving a quadratic equation | vedclass

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

Question

(C) Let the quadratic equation be $ax^2 + bx + c = 0$.The sum of the roots is given by $-\frac{b}{a}$ and the product of the roots is given by $\frac{

Vedclass · Accepted Answer

$128$

Vedclass · Answer

(C) Let the quadratic equation be $ax^2 + bx + c = 0$.The sum of the roots is given by $-\frac{b}{a}$ and the product of the roots is given by $\frac{c}{a}$.When the constant term is copied incorrectly,the sum of the roots remains unchanged because the sum depends only on the coefficients of $x^2$ and $x$.Given the roots are $5$ and $9$,the sum of the roots is $5 + 9 = 14$.Thus,$-\frac{b}{a} = 14$,which implies $b = -14a$.Another student copied the constant term $c = 12$ and the coefficient of $x^2$ as $a = 4$ correctly.Substituting $a = 4$ into $b = -14a$,we get $b = -14(4) = -56$.The correct equation is $4x^2 - 56x + 12 = 0$.The sum of the roots $s = -\frac{b}{a} = -\frac{-56}{4} = 14$.The product of the roots $p = \frac{c}{a} = \frac{12}{4} = 3$.The discriminant $\Delta = b^2 - 4ac = (-56)^2 - 4(4)(12) = 3136 - 192 = 2944$.Finally,calculating the required value: $\frac{\Delta}{3p + s} = \frac{2944}{3(3) + 14} = \frac{2944}{9 + 14} = \frac{2944}{23} = 128$.

Similar Questions

If a polynomial $P(x)$ of degree $4$ is given by $P(x) = 2x^4 + ax^3 + bx^2 + cx + d$ such that $P(1) = 4, P(2) = 7, P(3) = 12$,and $P(4) = 19$,then find the value of $P(5)$.

The sum of two roots of the equation $x^4-x^3-16x^2+4x+48=0$ is zero. If $\alpha, \beta, \gamma, \delta$ are the roots of this equation,then $\alpha^4+\beta^4+\gamma^4+\delta^4=$

The least value of $\frac{x^2y^2 - 2x^2y + 2x^2 + 2xy - 2x + 1}{x^2y + x}$ is $\lambda$,where $x, y \in R^+$ and $x^2y + x \neq 0$. Then:

If $x$ is real,then the maximum and minimum values of $\frac{x^2+14x+9}{x^2+2x+3}$ are respectively

If an angle $A$ of a $\Delta ABC$ satisfies $5 \cos A + 3 = 0$,then the roots of the quadratic equation $9x^2 + 27x + 20 = 0$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module