Question

Check whether 1 and 4 are the zeroes of the polynomial p(x) =x2 -5x +4
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Answer 1

Answer:

Both 1 and 4 are solutions for the given polynomial.

Step-by-step explanation:

$p(x) = {x}^{2} - 5x + 4$

Check for 1 :-------------------------

$p(1) = ( {1})^{2} - 5(1) + 4$

$p(1) = 1 - 5 + 4$

$p(1) = 0$

Hence, 1 is a solution of the polynomial.

Check for 4 :-----------------------

$p(4) = {(4)}^{2} - 5(4) + 4$

$p(4) = 16 - 20 + 4$

$p(4) = 0$

Hence, 4 is a solution of the polynomial.

Therefore, 1 and 4 are the solutions for this polynomial.

Hope it helps you.

Good Luck.

Answer 2

Question

Check whether 1 and 4 are the zeroes of the polynomial p(x) =x² -5x +4.

Answer

Let us consider 1 and 4 as zeroes of the given polynomial p(x)=x²-5x+4

Now,if x = 1

p (x) = x²-5x+4

p (1) =1²- 5 × 1 + 4

= 1 - 5 + 4

= 5 - 5

= 0------------①

Hence, 1 is a zero of the polynomial p(x)=x²-5x+4

Again, if x = 4

p (x) = x²-5x+4

p (4) = 4² - 5 × 4 + 4

= 16 - 20 + 4

= 20 - 20

= 0 -----------②

Hence, 4 is a zero of the polynomial p(x)=x²-5x+4

From equation ① and ② we find that both the given numbers are zeroes of the polynomial p (x) = x²-5x+4

Must know

★ The value that cause the particular polynomial to be zero is called the root of zero of the polynomial

★The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables).

★A polynomial function may have zero, one, or many zeros.