Question
The number of real values of x for which the equality |3x2+12x+6|=5x+16 holds good is
Answer: Option C
:
C
Equation|3x2+12x+6|=5x+16 ......(i)
when3x2+12x+6≥0⇔x2+4x≥−2
⇔ |x+2|2≥4−2⇔ |x+2|≥(√2)2
⇔ x + 2≤ - √2 or x + 2≥√2.......(ii)
Then (i) becomes 3x2+12x+6=5x+16
⇔ 3x2+7x−10=0⇒ x = 1, -103
But x = -103 does not satisfy (ii)
When 3x2+12x+6<0⇒ x2+4x>−2
⇒|x+2|≤√2⇒−√2−2≤x≤−2+√2....(iii)
⇒ 3x2+17x+22=0⇒ x=−2,−113
But x = - 113 does not satisfy (iii). So, 1 and -2 are the only solutions.
Was this answer helpful ?
:
C
Equation|3x2+12x+6|=5x+16 ......(i)
when3x2+12x+6≥0⇔x2+4x≥−2
⇔ |x+2|2≥4−2⇔ |x+2|≥(√2)2
⇔ x + 2≤ - √2 or x + 2≥√2.......(ii)
Then (i) becomes 3x2+12x+6=5x+16
⇔ 3x2+7x−10=0⇒ x = 1, -103
But x = -103 does not satisfy (ii)
When 3x2+12x+6<0⇒ x2+4x>−2
⇒|x+2|≤√2⇒−√2−2≤x≤−2+√2....(iii)
⇒ 3x2+17x+22=0⇒ x=−2,−113
But x = - 113 does not satisfy (iii). So, 1 and -2 are the only solutions.
Was this answer helpful ?
More Questions on This Topic :
Question 4. The roots of the equation √3x+1+1 = √x are....
Question 10. If x2+y2=25,xy=12,then complete set of x =....
Latest Videos
Latest Test Papers
Submit Solution