Question:
If the equation $2x^2 - (a+3)x + 8 = 0$ has equal roots, then one of the values of $a$ is
If the equation $2x^2 - (a+3)x + 8 = 0$ has equal roots, then one of the values of $a$ is
Updated On: Apr 8, 2024
- -9
- -5
- -11
- 11
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The Correct Option is C
Solution and Explanation
Given equation is $2 x^{2}+(a+3) x+8=0$
Here, $A=2, B=a+3$ and $C=8$
If roots are equal, then $B^{2}-4 A C=0$
$\Rightarrow (a+3)^{2}-4 \times 2 \times 8=0$
$\Rightarrow a^{2}+6 a+9-64=0$
$\Rightarrow a^{2}+6 a-55=0$
$\Rightarrow a^{2}+11 a-5 a-55=0$
$\Rightarrow (a+11)(a-5)=0$
$\therefore a=-11,5$
Here, $A=2, B=a+3$ and $C=8$
If roots are equal, then $B^{2}-4 A C=0$
$\Rightarrow (a+3)^{2}-4 \times 2 \times 8=0$
$\Rightarrow a^{2}+6 a+9-64=0$
$\Rightarrow a^{2}+6 a-55=0$
$\Rightarrow a^{2}+11 a-5 a-55=0$
$\Rightarrow (a+11)(a-5)=0$
$\therefore a=-11,5$
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
