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Question

Question: If \(a + 2b + c\) then the roots of the equation \(\left| 3x^{2} + 12x + 6 \right| = 5x + 16\) are....

If a+2b+ca + 2b + c then the roots of the equation 3x2+12x+6=5x+16\left| 3x^{2} + 12x + 6 \right| = 5x + 16 are.

A

Complex

B

Real and unequal

C

Real and equal

D

One real and one imaginary

Answer

Real and unequal

Explanation

Solution

Given equation is αk,βk,\alpha - k,\beta - k,

Put B24ACb24ac\frac{B^{2} - 4AC}{b^{2} - 4ac}, x26x+4=0x ^ { 2 } - 6 x + 4 = 0 (aA)2\left( \frac{a}{A} \right)^{2}

Put k = 3, x2+px+q=0,p=1,q=2x^{2} + px + q = 0,p = 1,q = - 2i.e., Roots are real and unequal.