Question

solve it by factorization
√3x^2+x+5=(x-3) ​

Answer 1

exactly two

Now, 3x2+x+5⩾0

This is because b2−4ac=1−4×5×3

=−59 (roots are imaginary)

3x2+x+5=(x−3)2=x2+9−6x and x−3⩾0

2x2+7x−4=0

2x2+8x−x−4=0

2x(x+4)−1(x+4)=0

(2x−1)(x+4)=0

x=21 and−4 but x≥3

∴ No solution.

Answer 2

Answer:

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Class 11>>Maths>>Complex Numbers and Quadratic Equations>>Quadratic Equations>>The equation √(3x^2 + x + 5) = x - 3 , w

Question

The equation 3x2+x+5=x−3, where x is real, has 

A

no solution.

B

exactly one solution.

C

exactly two solutions.

D

exactly four solutions.

Hard

JEE Mains

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Solution

Verified by Toppr

Correct option is A)

Now, 3x2+x+5⩾0

This is because b2−4ac=1−4×5×3

=−59 (roots are imaginary)

3x2+x+5=(x−3)2=x2+9−6x and x−3⩾0

2x2+7x−4=0

2x2+8x−x−4=0

2x(x+4)−1(x+4)=0

(2x−1)(x+4)=0

x=21 and−4 but x≥3