Question

if alpha, beta are zeroes of p(x)=2x2-x-6,then find the value of alpha-1+beta-1​

Answer 1

Answer:

- 3 / 2.

Step-by-step explanation:

We know,

         quadratic polynomials / equations represent sum and product of their roots as S and P in the equation in form of x^2 - Sx + P = 0.

 Therefore, here, in polynomial 2x^2 - x - 6

    Sum of roots = 1 / 2

    Product of roots = - 6 / 2 = - 3

⇒ α - 1 + β - 1

⇒ α + β - 1 - 1

⇒ α + β - 2

⇒ Sum of roots - 2

⇒ 1 / 2 - 2

⇒ ( 1 - 4 ) / 2

⇒ - 3 / 2

Answer 2

Answer:

$\boxed{\tt \alpha - 1 + \beta - 1 = \frac{-3}{2}}$

Step-by-step explanation:

Given that -

• α and β are the zeroes of the quadratic polynomial 2x² - x - 6.

We know that,

The standard form of the quadratic polynomial is ax² + bx + c. Here,

• a = 2
• b = - 1
• c = - 6

Sum of zeroes = $\sf \dfrac{-(coefficient \: of \: x)}{coefficient \: of \: x^2}$

⇒ α + β = $\dfrac{-(-1)}{2}$

⇒ α + β = $\dfrac{1}{2}$

Product of zeroes = $\sf \dfrac{constant \: term}{coefficient \: of \: x^2}$

⇒ αβ = $\dfrac{-6}{2}$

⇒ αβ = - 3

To find :

= α - 1 + β - 1

= α + β - 2

= $\dfrac{1}{2} - 2$

= $\dfrac{1 - 4}{2}$

= $\dfrac{-3}{2}$

Hence, the answer is -3/2.