Question

Show that 2 is not zero of the polynomial p(x)= x^2 +2x+5

Answer 1

Answer:

(2x2)+2x2+5

4+4+5

13isnot equal to 0

so 2 isnot it's zero

Answer 2

$\bold{\blue{\underline{\red{G}\pink{iv}\green{en}\purple{:-}}}}$

• P(x) = $\bold {x^2 + 2x + 5}$

• x = 2

$\bold{\blue{\underline{\red{Zeros}\pink{\:of\:}\green{\:the\:polynomials}\purple{:-}}}}$

• Zeros of the polynomial is the value of the variable for which when replaced in the polynomial the value for the polynomial changes to zero .

$\bold{\blue{\underline{\red{General}\pink{\:form \:of }\green{\:polynomial}\purple{:-}}}}$

• $\bold{a_{n}x^n + a_{n-1}x^{n-1} +...... + a_{2}x^2 + a_{1}x + a_{0}}$
• Where ' $\bold{a_{n} , a_{n-1} ...... a_{1} , a_{0}}$ ' are Real numbers and 'n' is an integer .

$\bold{\blue{\underline{\red{Q}\pink{uest}\green{ion}\purple{:-}}}}$

• To show that 2 is not a zero of the polynomial ' P(x) = $\bold {x^2 + 2x + 5}$ '

$\bold{\blue{\underline{\red{S}\pink{olut}\green{ion}\purple{:-}}}}$

• We have to show that P(2) $\neq$ 0

• P(2) = $\bold{2^2 + 2 \times 2 + 5}$

• P(2) = 4 + 4 +5
• P(2) = 13
• ∵ P(2) = 13 $\neq$ 0

• ∴ 2 is not a zero of the polynomial ' P(x) = $\bold {x^2 + 2x + 5}$ '