Find the value of k. if 12 is one of the zeroes of of the polynomial, 2x^2+kx+2 and find the other zero aswell
Answers
Step-by-step explanation:
2*12²+k*12+2=0
288+12k+2=0
290+12k=0
12k=0-290
k=-290/12
k= -24.16
Answer:
The value of k is -145/6
The other zero = 1/12
Step-by-step explanation:
Given :
12 is one of the zeroes of of the polynomial, 2x² + kx + 2
To find :
the value of k and the other zero
Solution :
Let p(x) = 2x² + kx + 2
12 is a zero of the polynomial.
p(12) = 0
Put x = 12,
2(12)² + k(12) + 2 = 0
2(144) + 12k + 2 = 0
288 + 12k + 2 = 0
12k + 290 = 0
12k = -290
k = -290/12
k = -145/6
Therefore, the value of k is -145/6
From the relation between zeroes and coefficients of a quadratic polynomial, we know
Sum of zeroes = -(x coefficient)/x² coefficient
Product of zeroes = constant term/x² coefficient
Let the other zero be 'α'
Product of zeroes = constant term/x² coefficient
12 × α = 2/2
12α = 1
α = 1/12
Therefore, the other zero is 1/12