If the equation (3 x)^2+(27 ×3^1 / p-15) x+4=0 has equal roots then p is (a) 0 (b) 2 (c) -(1)/(2

Name: Problem 141, Chapter 2: IIT-JEE Super Course in Mathematics
Uploaded: 2021-07-09T19:15:41-08:00
Duration: 4 min 5 s
Channel: Anas Venkitta
Description: If the equation (3 x)^2+(27 ×3^1 / p-15) x+4=0 has equal roots then p is (a) 0 (b) 2 (c) -(1)/(2) (d) 1

step 1 So in the given question we are told that if the equation given as 3x whole square plus 27 times

Question

If the equation $(3 x)^{2}+\left(27 \times 3^{1 / p}-15\right) x+4=0$ has equal roots then $p$ is (a) 0 (b) 2 (c) $-\frac{1}{2}$ (d) 1

   If the equation $(3 x)^{2}+\left(27 \times 3^{1 / p}-15\right) x+4=0$ has equal roots then $p$ is
(a) 0
(b) 2
(c) $-\frac{1}{2}$
(d) 1

IIT-JEE Super Course in Mathematics

Trishna Knowledge… 1st Edition

Chapter 2, Problem 141

Instant Answer

Solved by Expert Anas Venkitta

07/09/2021

Step 1

For a quadratic equation to have equal roots, the discriminant must be equal to zero. The discriminant is given by $b^2 - 4ac$. Show more…

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If the equation $(3 x)^{2}+\left(27 \times 3^{1 / p}-15\right) x+4=0$ has equal roots then $p$ is (a) 0 (b) 2 (c) $-\frac{1}{2}$ (d) 1

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Key Concepts

Quadratic Equation

A quadratic equation is an algebraic equation of the second degree, generally expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a is nonzero. The solutions or roots of a quadratic equation can be computed using various methods including factoring, completing the square, or the quadratic formula.

Discriminant

The discriminant in a quadratic equation, given by the expression b² - 4ac, determines the nature of its roots. If the discriminant is zero, the quadratic equation has equal (or repeated) roots, which is a key property used to set up conditions for solutions in such problems.

Exponential Expression

An exponential expression involves a base raised to a variable exponent, requiring the use of exponent rules to simplify or solve equations. In problems where parameters appear as exponents, understanding how to manipulate and solve exponential expressions is crucial.

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