Question

Given that if one zero of the quadratic polynomial x2-5x+k is -4, then the value of K is

Answer 1

Step-by-step explanation:

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 splitt :-

→ 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.

Answer 2

$\large{\underline{\bf{\purple{Given:-}}}}$

• ✦ p(x) = x² - 5x + k
• ✦ One zero is given = -4

$\large{\underline{\bf{\purple{To\:Find:-}}}}$

• ✦ we need to find the value of k

$\huge{\underline{\bf{\red{Solution:-}}}}$

we know that -4 is a zero of given polynomial.

So,

• x = -4

$\leadsto \rm\:\:(-4)^2-5(-4)+k=0$

$\leadsto \rm\:\:16+20+k=0$

$\leadsto \rm\:\:36+k=0$

$\leadsto \rm\:\:k= -36$

Verification:-

• p(x) = x² - 5x - 36

$\leadsto \rm\:\:x^2+4x-9x-36$

$\leadsto \rm\:\:x(x+4)-9(x+4)$

$\leadsto \rm\:\:(x-9)(x+4)$

$\leadsto \bf\:\:x=9\:\:or\:\:x=-4$

So ,we get the one zero of polynomial that is given.so our verification is correct.

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