The number of real solutions of the equation x2-x-3-9-10x-0 isA- 2B- 0C- 1D- none of these

The correct option is B 0Let nbsp;f(x)=x^2 x+3 D=1 12= 11 0 So, f(x) 0 for all x∈ℝ Also, (910)^x 0 nbsp;for all x∈ℝ Thus, L.H.S. of the given equation is ...

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Standard XII

Mathematics

Range of Quadratic Expression

The number of...

Question

The number of real solutions of the equation $x^{2} - x + 3 + {(\frac{9}{10})}^{x} = 0$ is

2

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0

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1

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none of these

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Solution

The correct option is B $0$
Let $f (x) = x^{2} - x + 3$
$D = 1 - 12 = - 11 < 0$
So, $f (x) > 0$ for all $x \in R$
Also, ${(\frac{9}{10})}^{x} > 0$ for all $x \in R$
Thus, L.H.S. of the given equation is always positive.
Hence, there is no solution.

Suggest Corrections

The number of real solutions of the equation x2−x+3+(910)x=0 is

The correct option is B 0Let f(x)=x2−x+3 D=1−12=−11<0 So, f(x)>0 for all x∈R Also, (910)x>0 for all x∈R Thus, L.H.S. of the given equation is always positive. Hence, there is no solution.

The number of real solutions of the equation $x^{2} - x + 3 + {(\frac{9}{10})}^{x} = 0$ is

The correct option is B $0$
Let $f (x) = x^{2} - x + 3$
$D = 1 - 12 = - 11 < 0$
So, $f (x) > 0$ for all $x \in R$
Also, ${(\frac{9}{10})}^{x} > 0$ for all $x \in R$
Thus, L.H.S. of the given equation is always positive.
Hence, there is no solution.