Question

if alpha and beta are the zeros of the quadratic polynomial f (x)=X square + X - 2 then find the value of Alpha minus beta ​

Answer 1

Answer:

$x2 + x - 2 = 0 \\ \\ x2 + 2x - x - 2 = 0 \\ \\ x(x + 2) - 1(x + 2) = 0 \\ \\ (x + 2) = 0 \: \: \: (x - 1) = 0 \\ \\ x = - 2 \: \: \: \: x = 1 \\ \\ \alpha = - 2 \: \: \: \beta = 1$

alpha- beta = -3

My answer is correct so please mark as BRAINLIEST

please mark as BRAINLIEST

Answer 2

Given:

A quadratic polynomial f(x)= x²+x-2 whose zeroes are α and β.

To Find:

• Value of α-β

Solution:

Given polynomial,f(x)=x²+x-2= x²-(-1)x+(-2)

We know that,

• $\mathrm{a-b=\sqrt{(a+b)^{2}-4ab}}$

• A quadratic polynomial can be expressed as

$\boxed{\sf{x^{2}-(Sum\:of\:Zeroes)x+(Product\:of\:Zeroes)}}$

So, on comparing given polynomial f(x) with above expression, we get

➺ Sum of Zeroes=α+β= -1

➺ Product of Zeroes=αβ= -2

Now,

$\longrightarrow\mathrm{\alpha-\beta=\sqrt{(\alpha+\beta)^{2}-4\alpha\beta}}$

$\longrightarrow\mathrm{\alpha-\beta=\sqrt{(-1)^{2}-4(-2)}}$

$\longrightarrow\mathrm{\alpha-\beta=\sqrt{1+8}}$

$\longrightarrow\mathrm{\alpha-\beta=\sqrt{9}}$

$\longrightarrow\mathrm{\alpha-\beta=\pm3}$

$\longrightarrow\mathrm\pink{\alpha-\beta=3,-3}$

Hence, the values of α-β are 3 and -3.