Question

.The number to be added to the polynomial x^2 - 5x+4 , so that 3 is the zero of the polynomial is
2
-2
0
3

solve

Answer 1

Answer:

2

Step-by-step explanation:

Let k be added to the polynomial.

Given Equation is p(x) = x^2 - 5x + (4 + k).

If 3 is the zero of the polynomial, then the equation will become p(3) = 0

p(3) = (3)^2 - 5(3) + (4 + k) = 0

9 - 15 + 4 + k = 0

- 6 + 4 + k = 0

-2 + k = 0

k = 2.

Therefore the number to be added to the polynomial is 2.

Answer 2

Answer:

$\Large{\underline{\underline{\bf{Option\:A:\:2}}}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• p(x) = x² - 5x +4

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Number to be added to p(x) so 3 is the zero of the polynomial

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let the constant a be added to the polynomial p(x). Hence p(x) becomes

p(x) = x² - 5x + 4 +a

→ Since 3 is a zero of the polynomial,

p(3) = (3)² - 5 × 3 + 4+a = 0

      = 9 -15 + 4+ a = 0

      = a - 2 =0

      a = 2

→ Therefore 2 must be added to p(x) so that 3 is a zero of the polynomial.

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ A quadratic polynomial is of the form ax² + bx + c and has two zeros.

→ The degree of a quadratic polynomial is 2.

→ Some examples of quadratic polynomial

• 2x² + 3x +9
• x²-5
• 4x² + 7x