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Quadratic Equations

Section: Mathematics

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Question : 51 of 51

Marks: +1, -0

If the roots of the quadratic equation

x^2-35 x+c=0

are in the ratio

2: 3

c=6 K

K=

[AP EAPCET 18 May 2024 Shift 1]

49
14
21
7

Solution:

The roots of the quadratic equation

x^2-35 x+c=0

are given to be in the ratio 2:3.

Let's assume the roots are

2 \alpha

and

3 \alpha

.

The sum of the roots is given by the equation:

2 \alpha+3 \alpha=5 \alpha=35

Solving for

\alpha

, we get:

\alpha=7

The product of the roots can be expressed as:

(2 \alpha)(3 \alpha)=6 \alpha^2=c

Substituting the value of

\alpha

, we find:

c=6 \times 7^2=6 \times 49

Given that

c=6 K

, we equate to find

K

:

6 \times 49=6 K

K=49

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