Question

13. What number should be added to the polynomial x? - 5x + 4, so that 3 is the zero of the
polynomial?
(a) 2
(b)-2
(c) 1
(d)-1​

Answer 1

Answer:

2

Step-by-step explanation:

Let the required number be 'a'.  If 'a' is added to given polynomial, then 3 is the zero of polynomial.

∴ The statement is now 'x² - 5x + 4 + a' has a zero 3,  it means f(3) = 0.

⇒ f(3) = 0

⇒ (3)² - 5(3) + 4 + a =  0

⇒ 9 - 15 + 4 + a = 0

⇒ - 2 + a = 0

⇒ a = 2

   hence the required number is 2.

option (a)

Answer 2

Given :-

• 3 is the zero of the polynomial equation $\sf x² - 5x + 4$

To Find :-

• What number should be added to this polynomial ?

Answer :-

• $\sf 2$

Explanation :-

• Consider that the number added to this polynomial equation is k.

• so, we can write like this,

• p(x) = (x² - 5x + 4 ) + k

• Now, We have zero of this polynomial equation
• Hence, p(3) = 0 , now in equation

• $\sf p(x) = (x² - 5x + 4) +k$

• $\sf p(3) = \bigg((3)² - 5(3) + 4 \bigg) + k$

• $\sf 0 = ( 9 - 15 + 4 ) + k$

• $\sf 0 = 13 -15 + k$

• $\sf 0 = -2 + k$

• $\sf \fbox{k= 2 }$

hence,

The number 2 is added to this polynomial equation.

I hope it helps you ❤️✔️