Sachin and Rahul attempted to solve a quadrat | vedclass

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

Question

(A) Let the quadratic equation be $ax^{2} + bx + c = 0$.Sachin made a mistake in the constant term,so the sum of the roots is correct.Sum of roots $=

Vedclass · Accepted Answer

$6, 1$

Vedclass · Answer

(A) Let the quadratic equation be $ax^{2} + bx + c = 0$.Sachin made a mistake in the constant term,so the sum of the roots is correct.Sum of roots $= 4 + 3 = 7$.Rahul made a mistake in the coefficient of $x$,so the product of the roots is correct.Product of roots $= 3 	imes 2 = 6$.The correct quadratic equation is $x^{2} - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values,we get $x^{2} - 7x + 6 = 0$.Factoring the equation: $x^{2} - 6x - x + 6 = 0 \implies x(x - 6) - 1(x - 6) = 0 \implies (x - 6)(x - 1) = 0$.Thus,the correct roots are $6$ and $1$.

Sachin and Rahul attempted to solve a quadratic equation. Sachin made a mistake in writing down the constant term and ended up with roots $(4, 3)$. Rahul made a mistake in writing down the coefficient of $x$ and ended up with roots $(3, 2)$. The correct roots of the equation are:

Similar Questions

If $\alpha$ and $\beta$ are the roots of $9x^2 + 6x + 1 = 0$,then the equation with the roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $3x^3 - 9x^2 + 5x - 7 = 0$,then what is the value of $\alpha + \beta + \gamma$?

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

If $\alpha, \beta, \gamma$ are the roots of $x^3+4x+1=0$,then the equation whose roots are $\frac{\alpha^2}{\beta+\gamma}, \frac{\beta^2}{\gamma+\alpha}, \frac{\gamma^2}{\alpha+\beta}$ is

If the roots of the equations $ax^2 + bx + c = 0$ and $px^2 + qx + r = 0$ are $\alpha_1, \alpha_2$ and $\beta_1, \beta_2$ respectively,and the system of linear equations $\alpha_1y + \alpha_2z = 0$ and $\beta_1y + \beta_2z = 0$ has a non-zero solution,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module