Question

If a and b are the zeroes of p (x) =x ²- 5 x + 6, then value of a + b - 3ab is

Answer 1

AnswEr:-

Your Answer Is -13.

ExplanaTion:-

Given:-

A polynomial,

$\bullet\:\: \tt x^2-5x+6$

a and b are zeroes of the given polynomial.

To Find:-

• The value of $\tt a+b-3ab.$

Concepts Used:-

In a quadratic polynomial,

$\\ \\ \rm\large\bullet\underline{Sum\:\:Of\:\:Zeores,}\\ \\ \tt = \dfrac{-b}{a}.\\ \\ \rm\large\bullet\underline{Product\:\:Of\:\:Zeroes,}\\ \\ \tt = \dfrac{c}{a}.$

Where,

• a = Coefficient of x².

• -b = -Coefficient of x.

• c = Constant term.

So Here,

• a = 1.

• -b = -(-5) = 5.

• c = 6.

Therefore,

$\\ \\ \tt\mapsto a + b = \dfrac{5}{1}. \\ \\ \tt\mapsto a + b = 5...(1) \\ \\ \rm \: and \\ \\ \tt\mapsto a \times b = \dfrac{6}{1} . \\ \\ \tt\mapsto ab = 6...(2) \\ \\ \rm \: so \\ \\ \tt\longrightarrow a + b - 3ab = 5 - 3(6) .\\ \\ \rm[from \: \: (1) \: \: and \: \: (2)]. \\ \\ \tt\longrightarrow a + b - 3ab = 5 - 18. \\ \\ \tt\longrightarrow \boxed{\underline{\underline{a + b - 3ab = - 13.}}}$

$\rm{\therefore\:\: Your\:\:Answer\:\:Is\:\: -13}.$