Question

If a and B are zeros of the polynomia
1
P(x) = 6x2 – 5x + k such that a - b = 1/b

Answer 1

Answer:

K=1

Step-by-step explanation:

According to the question ,a and b are zeros of$P(x)=6x^{2}-5x+k$

Sum of zeros =$a+b= -[\frac{-5}{6}]=\frac{5}{6}$------(1)

$a-b=\frac{1}{b}$------(2)

Adding equations (1) and (2),

we get,

$2a=1$

$a=\frac{1}{2}$

On putting the values of a in equation (2),

we get,

$\frac{1}{2}-b=\frac{1}{6}$

$b=\frac{1}{2}-{1}{6}$

$b=\frac{2}{2}=\frac{1}{6}$

$ab=\frac{k}{6}=\frac{1}{2}×\frac{1}{3}$

Hence,

$\boxed{k=1}$

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