Question

equation .​Previous year IIT jee Question
Chapter :- complex number and quadratic​

Answer 1

EXPLANATION.

Number of real roots.

$\implies 3^{2x^{2} - 7x + 7} = 9$

As we know that,

We can write equation as,

$\implies 3^{2x^{2} - 7x + 7} = (3)^{2}$

⇒ 2x² - 7x + 7 = 2.

⇒ 2x² - 7x + 7 - 2 = 0.

⇒ 2x² - 7x + 5 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 2x² - 5x - 2x + 5 = 0.

⇒ x(2x - 5) - 1(2x - 5) = 0.

⇒ (x - 1)(2x - 5) = 0.

⇒ x = 1 and x = 5/2.

As we can see that 2 real roots exists.

Option [B] is correct answer.

Answer 2

b) 2

Step-by-step explanation:

Q.

The number of real roots of 3^2x²-7x+7 = 9

Solution -

${3}^{2 {x}^{2} - 7 + 7} = 9 \\ \\ = > {3}^{2 {x}^{2} - 7x + 7} = {3}^{2} \\ \\ = > 2 {x}^{2} - 7x + 7 = 2 \\ \\ = > 2 {x}^{2} - 7x + 7 - 2 = 0 \\ \\ = > {2x}^{2} - 7x + 5 = 0$

=> 2x² - 2x - 5x + 5 = 0

=> 2x(x - 1) - 5(x - 1) = 0

=> (x - 1) (2x - 5) = 0

.

root no. 1 -

x - 1 = 0

=> x = 1

.

Root no. 2 -

2x - 5 = 0

=> 2x = 5

=> x = 5/2

.

Hence there are two real roots of the equation.

hope it helps.