The number of real solution of- -2 x - x 2-3-1 isA- 0B- 2C- 3D- 4

The correct option is B 2 Given equation:|2x x^2 3|=1 (i)2x x^2 3=1 ⇒ 2x x^2 4=0 ⇒ x^2 2x+4=0 ⇒ (x 2)^2=0 ⇒ x = 2, 2 (ii) 2x+x^2+3=1 ⇒ x^2 2x+2=0 ⇒ x^2 2x+1 ...

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Standard XIII

Mathematics

Roots of a Quadratic Equation

The number of...

Question

The number of real solution of: $| 2 x - x^{2} - 3 | = 1$ is

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Solution

The correct option is B
2

$Given equation : | 2 x - x^{2} - 3 | = 1 (i) 2 x - x^{2} - 3 = 1 \Rightarrow 2 x - x^{2} - 4 = 0 \Rightarrow x^{2} - 2 x + 4 = 0 \Rightarrow (x - 2)^{2} = 0 \Rightarrow x = 2, 2 (i i) - 2 x + x^{2} + 3 = 1 \Rightarrow x^{2} - 2 x + 2 = 0 \Rightarrow x^{2} - 2 x + 1 + 1 = 0 \Rightarrow (x - 1)^{2} - i^{2} = 0 \Rightarrow (x - 1 + i) (x - 1 - i) = 0 \Rightarrow x = 1 - i, 1 + i Hence, the real solutions are 2, 2.$

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The number of real solution of:|2x−x2−3|=1 is

The correct option is B 2 Given equation:|2x−x2−3|=1(i)2x−x2−3=1⇒2x−x2−4=0⇒x2−2x+4=0⇒(x−2)2=0⇒x=2,2(ii)−2x+x2+3=1⇒x2−2x+2=0⇒x2−2x+1+1=0⇒(x−1)2−i2=0⇒(x−1+i)(x−1−i)=0⇒x=1−i,1+iHence, the real solutions are 2, 2.

The number of real solution of: $| 2 x - x^{2} - 3 | = 1$ is