Question

if one zero of the quadratic polynomial x²+5x+k is 2 then the other zero will be​

Answer 1

Answer:

Given -

One zero of quadratic polynomial x² - 5x + k is -4

To Find -

Value of k

Now,

→ p(x) = x² - 5x + k

→ p(-4) = (-4)² -5×(-4) + k = 0

→ 16 + 20 + k = 0

→ k = -36

Hence,

The value of k is -36

Verification :-

→ x² - 5x + (-36)

→ x² - 5x - 36

By middle term split :-

→ x² + 4x - 9x - 36

→ x(x + 4) - 9(x + 4)

→ (x - 9)(x + 4)

Zeroes are -

→ x - 9 = 0 and x + 4 = 0

→ x = 9 and x = -4

Here, One zero comes same as given in the question it shows that our answer is absolutely correct.

Step-by-step explanation:

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Answer 2

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To Solve:

• If one zero of the quadratic polynomial x²+5x+k is 2 then the other zero will be

Solⁿ:

• Put value of zero in the eqⁿ.
• Find k
• Then factorize the new eqⁿ formed and you will get the other Zero

1st Step:

x² + 5x + k = 0

p(x) = 2

= (2)² + 5(2) + k = 0

= 4 + 10 + k = 0

= 14 + k = 0

= k = -14

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New Eqⁿ: x² + 5x - 14 = 0

• Factorizing the new eqⁿ:

x² + 5x - 14 = 0

x² + 7x - 2x - 14 = 0

x (x + 7) -2 (x + 7) = 0

(x + 7) (x - 2) = 0

x = -7ㅤㅤx = 2

So, The Other zero is -7.

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