If x^2-3ax+14=0 and x^2+2ax-16=0 have a commo | vedclass

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

Question

(B) Let the common root be $\alpha$. Then,$\alpha^2-3a\alpha+14=0$ and $\alpha^2+2a\alpha-16=0$. Subtracting the two equations: $(\alpha^2-3a\alpha+14

Vedclass · Accepted Answer

$90$

Vedclass · Answer

(B) Let the common root be $\alpha$. Then,$\alpha^2-3a\alpha+14=0$ and $\alpha^2+2a\alpha-16=0$. Subtracting the two equations: $(\alpha^2-3a\alpha+14) - (\alpha^2+2a\alpha-16) = 0$ $-5a\alpha + 30 = 0 $ $\Rightarrow 5a\alpha = 30 $ $\Rightarrow \alpha = \frac{6}{a}$. Substituting $\alpha = \frac{6}{a}$ into the first equation: $(\frac{6}{a})^2 - 3a(\frac{6}{a}) + 14 = 0$ $\frac{36}{a^2} - 18 + 14 = 0$ $\frac{36}{a^2} = 4 \Rightarrow a^2 = 9$. Now,$a^4+a^2 = (a^2)^2 + a^2 = (9)^2 + 9 = 81 + 9 = 90$.

If $x^2-3ax+14=0$ and $x^2+2ax-16=0$ have a common root,then $a^4+a^2=$

Similar Questions

If $ax^2 + bx + c = 0$ and $bx^2 + cx + a = 0$ have a common root and $a, b, c$ are non-zero real numbers,then $\frac{a^3 + b^3 + c^3}{abc} = $

The value of $a$ for which the equations $x^3+ax+1=0$ and $x^4+ax^2+1=0$ have a common root is

If $x^2+3x-2k=0$ and $x^2-2x-7k=0$ have a non-zero common root,then the positive root of the equation $kx^2+(k+2)x-(k+1)=0$ is

If the equations $x^2 + bx + c = 0$ and $x^2 + cx + b = 0$ $(b \neq c)$ have a common root,then:

If the equations $x^2 + px + q = 0$ and $x^2 + qx + p = 0$ have a common root,then $p + q + 1 = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module