Question

if a and b are the zeroes of a polynomial such that a+b=2 and ab=-5,then find the polynomial

pls ans fast​

Answer 1

Answer:

i think the question is wrong

Step-by-step explanation:

5 is a prime number it will come only in 5 tables how ab=5

Answer 2

Answer:

x²-2x-5

Step-by-step explanation:

Let 'a' and 'b' be zeroes of the polynomial,

p(x) = ax² + bx +c

Given,

Sum of the zeroes, a+b = 2

product of the zeroes, ab = -5

Here,

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

$ab = - 5 = \frac{ - 5}{1} = \frac{c}{a}$

We got ,

a = 1,

b = (-2) and

c= (-5)

So the polynomial in the form ax²+bx+c is

1x² + (-2)x + (-5)

=> x² -2x -5

Check:-

Solving the quadratic equation x²-2x-5, we get

$\frac{ - b± \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\frac{ - ( - 2)± \sqrt{ {2}^{2} - 4 \times 1 \times - 5} }{2 \times 1}$

$\frac{2± \sqrt{4 + 20} }{2}$

$\frac{2± \sqrt{24} }{2}$

$\frac{2± \sqrt{4 \times 6} }{2}$

$\frac{2±2 \sqrt{6} }{2}$

$\frac{2(1± \sqrt{6)} }{2}$

$1± \sqrt{6}$

so, roots are (1+√6) and (1-√6).

Sum of roots = 1+ √6+ 1 -√6 = 2

product of roots = (1+√6) (1-√6) = 1²-√6² = 1-6 = -5

Hence the answer.

Hope this helps you:)