If the equations x^2 + 2x + 3 = 0 and ax^2 + | vedclass

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

Question

(A) The given equation is $x^2 + 2x + 3 = 0$. Calculating the discriminant $D = b^2 - 4ac = (2)^2 - 4(1)(3) = 4 - 12 = -8$. Since $D < 0$,the roots of

Vedclass · Accepted Answer

$1:2:3$

Vedclass · Answer

(A) The given equation is $x^2 + 2x + 3 = 0$. Calculating the discriminant $D = b^2 - 4ac = (2)^2 - 4(1)(3) = 4 - 12 = -8$. Since $D If two quadratic equations have a common root and the coefficients are real,then the imaginary roots must occur in conjugate pairs. Therefore,if one root is common,both roots must be common. For two equations $a_1x^2 + b_1x + c_1 = 0$ and $a_2x^2 + b_2x + c_2 = 0$ to have the same roots,the ratio of their coefficients must be equal: $\frac{a}{1} = \frac{b}{2} = \frac{c}{3} = k$. This implies $a = k, b = 2k, c = 3k$. Thus,the ratio $a:b:c = k:2k:3k = 1:2:3$.

If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$,where $a, b, c \in R$,have a common root,then $a:b:c = $ ...

Similar Questions

If $A.M.$ of the roots of a quadratic equation is $8/5$ and $A.M.$ of their reciprocals is $8/7$,then the equation is

If the product of the roots of the equation $(a + 1)x^2 + (2a + 3)x + (3a + 4) = 0$ is $2$,then the sum of the roots is:

Solve the given two equations and select the correct option.
$I. 3x^2 + 5x - 2 = 0$
$II. 2y^2 - 7y + 5 = 0$

The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module