If the equations ax^2 + bx + c = 0 (a, b, c i | vedclass

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

Question

(B) Given that the equations $ax^2 + bx + c = 0$ and $2x^2 + 3x + 4 = 0$ have a common root.For two quadratic equations $a_1x^2 + b_1x + c_1 = 0$ and

Vedclass · Accepted Answer

$2 : 3 : 4$

Vedclass · Answer

(B) Given that the equations $ax^2 + bx + c = 0$ and $2x^2 + 3x + 4 = 0$ have a common root.For two quadratic equations $a_1x^2 + b_1x + c_1 = 0$ and $a_2x^2 + b_2x + c_2 = 0$ to have a common root,the coefficients must be proportional if both roots are common,or we can use the condition for a single common root.However,in this case,the discriminant of the second equation $2x^2 + 3x + 4 = 0$ is $D = b^2 - 4ac = 3^2 - 4(2)(4) = 9 - 32 = -23$.Since $D Therefore,the two equations must be proportional:$\frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k$This implies $a = 2k$,$b = 3k$,and $c = 4k$.Thus,the ratio $a : b : c = 2k : 3k : 4k = 2 : 3 : 4$.

If the equations $ax^2 + bx + c = 0$ $(a, b, c \in R, a \ne 0)$ and $2x^2 + 3x + 4 = 0$ have a common root,then $a : b : c$ equals

Similar Questions

Solve the given two equations and select the correct answer from the given options.
$I.$ $81x^2 - 9x - 2 = 0$
$II.$ $56y^2 - 13y - 3 = 0$

If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b = 0$ and if $\alpha^n + \beta^n = V_n$,then

Solve the given two equations and select the correct option.
$I.$ $7x + 3y = 26$
$II.$ $2x + 17y = -41$

Solve the given system of three linear equations and select the correct relationship between $x, y,$ and $z$ from the given options.
$I. 7x + 6y + 4z = 122$
$II. 4x + 5y + 3z = 88$
$III. 9x + 2y + z = 78$

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}-3 \lambda x+\lambda^{2}=0,$ find $\lambda$ if $\alpha^{2}+\beta^{2}=\frac{7}{4}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module