Question

TRUE OR FALSE 3 is one of the zeroes of the polynomial p(x)=x²-8x+15.
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Answer 1

Answer:

yes...because 3^2-8x3+15=0

Answer 2

★ Answer:-

True, 3 is one of the zeroes of the polynomial p(x)=x²-8x+15.

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★ Explanation:-

If 3 is a factor of the given equation, then after putting value of x=3 in the equation the answer must be 0 because function of zero is to divide the polynomial without leaving remainder.

So let's verify!!

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We have polynomial:

⇒  p(x)=x²-8x+15

Put the value of x to be 3.

⇒  0=(3)²-8(3)+15

Now simplify it:

⇒  0=9-24+15

⇒  0=24-24

⇒  0=0

Hence verified that 3 is a zero.

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★ Alternate Method:-

There is another method to find if 3 is a factor of given polynomial. We can find value of zeroes of the polynomial by factorising it

So  start!!

Given polynomial:

⇒  p(x)=x²-8x+15

Middle term splitting:

⇒  p(x)=x²-3x-5x+15

⇒  p(x)=x(x-3)-5(x-3)

⇒  p(x)=(x-3)(x-5)

⇒  x=3,5

Since one of the zero of the polynomial is 3, the given statement is true.

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★ Learn More!!

Quadratic Formula:-

$\Large\underline{\boxed{\sf{x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}}\bigstar$

This is a formula to find roots of a given equation. You can use this equation when the given equation is complicated or the values are in square root.

Here in this formula:-

• a is coefficient of x².

• b is coefficient of x.

• c is constant term.

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