MHT CET202415 May 2024Morning ShiftMathematicsQuadratic EquationActual

The equation e ^ x - e ^ - x =4 has _______ solutions.

Options

Correct answer

D. no

Step-by-step solution

e ^ x -e^ - x -4=0 Let e ^ x =y , then the given equation can be written as y^2-4 y-1=0 y=2 5 But the value of y= e ^ x is always positive, so aligned & y=2+ 5 & e ^ x =2+ 5 & e ^ x e & x 1 aligned aligned & [ 2 5 ] & [ 2+ 5 e ] aligned which is not possible, since x cannot be greater than 1. Hence, no real value of x satisfies the given equation.

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025 If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025 If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025 Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025 If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025 If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025 The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025 If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All MHT CET PYQs