Question

If a and b are the zeroes of the quadratic polynomial 2x2-x+3,then find the value of (1)a+b​

Answer 1

GIVEN :–

• A quadratic equation 2x² - x + 3 = 0 have two roots as a and b.

TO FIND :–

• Value of a + b = ?

SOLUTION :–

$\\ \implies \sf \: 2 {x}^{2} - x + 3 = 0$

• We know that if a quadratic equation ax² + bx + c = 0 then –

$\\ \implies \sf sum \: \: of \: \: roots = - \dfrac{coffieciant \: \: of \: \: x}{coffieciant \: \: of \: \: {x}^{2} } = - \dfrac{b}{a}$

• Here –

$\\ \: \: \: \: \: \: {\huge{.}} \: \: \: \sf a = 2$

$\\ \: \: \: \: \: \: {\huge{.}} \: \: \: \sf b = -1$

$\\ \: \: \: \: \: \: {\huge{.}} \: \: \: \sf c = 3$

• So that –

$\\ \implies \sf a + b= - \dfrac{( - 1)}{2 }$

$\\ \implies \large { \boxed{ \sf a + b= \dfrac{ 1}{2 }}}$

EXTRA INFORMATION :–

$\\ \longrightarrow \: \: \sf sum \: \: of \: \: roots = - \dfrac{coffieciant \: \: of \: \: x}{coffieciant \: \: of \: \: {x}^{2} }$

$\\ \longrightarrow \: \: \sf product \: \: of \: \: roots = \dfrac{constant \: \: term}{coffieciant \: \: of \: \: {x}^{2} }$

Answer 2

Given:

• a & b are the zeroes of the quadratic polynomial 2x² - x + 3

To find:

• a + b

Solution:

Given ,

To find a + b

Here, a & b are the roots

That means the question is about to find the sum of roots

We know that

Sum of roots = - b/a

Where

• b : coefficient of x
• a : coefficient of x²

Give quadratic polynomial : 2x² - x + 3

Here,

b : coefficient of x = - x = - 1x = - 1

a : coefficient of x² = 2

Substituting the values we have

→ Sum of roots (a + b) = - ( - 1)/2

→ Sum of roots (a + b) = 1/2. [ .answer ]

Hence, a + b = 1/2.