Question

If one zero of the quadratic polynomial x2+ 3x + k is 2, then the value of k is


Select one:
a. 10
b. -10
c. 5
d. -5

Answer 1

Correct Question:

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is:

Working out:

We have a polygonal of degree 2 whose one zero is given to us. The constant term here is considered as an variable of k.

• Polynomial = x² + 3x + k
• One of the zero is 2

By using Euclid's division lemma we know that, Dividend = Divisor × Quotient + Remainder. A zero of a given Polynomial make the polynomial as 0, if we put the value of the zero in the place of variable like x or y or a etc.

Here,

• f(x) = x² + 3x + 2
• x = 2 (As 2 is a zero of the polynomial)
• Then f(2) = 0

⇛ f(2) = 0

⇛ x² + 3x + k = 0

Plugging 2 in place of x in the polynomial,

⇛ 2² + 3(2) + k = 0

⇛ 4 + 6 + k = 0

⇛ 10 + k = 0

⇛ k = -10

So the required value of k is:

$\huge{ \boxed{ \purple{ \sf{ - 10(Option \: B)}}}}$

And we are done !!