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

Let $[r]$ denote the greatest integer not exceeding $r$. The roots of the equation $3 x^2 + 6 x + 5 + \alpha (x^2 + 2 x + 2) = 0$ are complex numbers whenever $\alpha > L$ or $\alpha < M$. If $(L - M)$ is minimum,then the greatest value of $[r]$ such that $L y^2 + M y + r < 0$ for all $y \in R$ is:

If $\frac{x-P}{x^2-3x+2}$ takes all real values for $x \in \mathbb{R} \setminus \{1, 2\}$,then the range of $P$ is

If $x$ is complex,the expression $\frac{x^2+34x-71}{x^2+2x-7}$ takes all values which lie in the interval $(a, b)$,find the value of $a$ and $b$.

The population of cattle in a farm increases such that the difference between the population in year $n+2$ and that in year $n$ is proportional to the population in year $n+1$. If the populations in years $2010, 2011$ and $2013$ were $39, 60$ and $123$ respectively,then the population in $2012$ was:

For real values of $x$,the range of $\frac{x^2+2x+1}{x^2+2x-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module