Question

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

Answer 1

GIVEN :-

• one zero of quadratic polynomial is 2
• A Quadratic polynomial x² + 3x + k.

TO FIND :-

• The value of k.

SOLUTION :-

➣ Let p(x) = x² + 3x + k = 0

➣ p(2) = x² + 3x + k = 0

➣ (2)² + 3 × 2 × k = 0

➣ 4 + 6 × k = 0

➣ 10k = 0

➣ k = -10

Hence the value of k is - 10 .

ADDITIONAL INFORMATION :-

➠ Remainder theorem :- If p(x) is is any polynomial of degree greater than or equal to 1 and p(x) is divided by the linear polynomial x - a , Then the reminder is p(a).

➠ Factor theorem :- x - a is a factor of the polynomial p(x) , If p(a) = 0. Also, If x - a is a Factor of p(x) , Then p(a) = 0.

➠Every linear polynomial in one variable has a unique zero, a non - zero constant polynomial has no zero, and every real number is a zero of the zero polynomial.

Answer 2

Given ,

• The one zero the quadratic polynomial (x)² + 3x + k is 2

Let ,

P(x) = (x)² + 3x + k

Thus ,

P(2) = 0

(2)² + 3 × 2 + k = 0

4 + 6 + k = 0

10 + k = 0

k = -10

$\therefore$ The value of k is -10