The number of real solutions of the equation 9-10 x -3- x - x 2 isA- oneB- twOC- more than twoD- none

The correct option is D none( 9/10 )^x = 3 + x x^2 ⇒ ( 9/10 )^x = { ( x 1/2 )^2 + 11/4} ∵ LHS is always positive and RHS is always negative for all x. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Range of Quadratic Expression

The number of...

Question

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

none

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

one

No worries! We‘ve got your back. Try BYJU‘S free classes today!

two

No worries! We‘ve got your back. Try BYJU‘S free classes today!

more than two

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A none
${(\frac{9}{10})}^{x} = - 3 + x - x^{2} \Rightarrow {(\frac{9}{10})}^{x} = - {{(x - \frac{1}{2})}^{2} + \frac{11}{4}}$
$∵$ LHS is always positive and RHS is always negative for all x.
Hence no solution.

Suggest Corrections

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

The correct option is A none(910)x=−3+x−x2⇒(910)x=−{(x−12)2+114} ∵ LHS is always positive and RHS is always negative for all x. Hence no solution.

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

The correct option is A none
${(\frac{9}{10})}^{x} = - 3 + x - x^{2} \Rightarrow {(\frac{9}{10})}^{x} = - {{(x - \frac{1}{2})}^{2} + \frac{11}{4}}$
$∵$ LHS is always positive and RHS is always negative for all x.
Hence no solution.