Question

If -5 is a root of the quadratic equation 2x²+px-15=0 and the quadratic equation p(x²+x)+k=0 has equal root. Find the value of k

Answer 1

Answer:

K=- 140

Step-by-step explanation:

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Answer 2

Given:-

• -5 is a root of the quadratic equation 2x²+px-15=0 and the quadratic equation p(x²+x)+k=0 has equal root.

To find:-

• Find the value of k..?

Solutions:-

• The given quadratic equation is 2x² + px - 15 = 0, and one root is -5.

Then, the given equation

=> 2(-5)² + p(-5) - 15 = 0

=> 2(25) - 5p - 15 = 0

=> 50 - 5p - 15 = 0

=> 35 - 5p = 0

=> -5p = -35

=> p = -35/-5

=> p = 7

The quadratic equation p(x² + x) + k = 0, has equal roots.

Putting the value of p, we get.

=> 7(x² + x) + k = 0

=> 7x² + 7x + k = 0

Here,

• a = 7
• b = 7
• c = k

We know that;

• D => b² - 4ac

Putting the value of a = 7, b = 7 and c = k

• D => b² - 4ac

=> (7)² - 4(7)(k)

=> 49 - 28k

The given equation will have real are equal roots,

Thus,

=> 49 - 28k = 0

=> 28k = 49

=> k = 49/28

=> k = 7/4

Hence, the value of k is 7/4.