Question

F(x) = 2x^2 - 3x + 1, find α-β? With complete solutions

Answer 1

Answer:

F(x) = 2x² - 3x + 1

Here, we have ;

Sum of zeroes = - b/a

⇒ α + β = - (-3)/2

⇒ α + β = 3/2

Product of zeroes = c/a

⇒ αβ = 1/2

We know that ;

$\boxed{ (\alpha - \beta ) {}^{2} = ( \alpha + \beta ) {}^{2} - 4 \alpha \beta } \\ \\ \rightarrow (\alpha - \beta ) {}^{2} = ( \frac{3}{2} ) {}^{2} - 4 \times \frac{1}{2} \\ \\ \rightarrow (\alpha - \beta ) {}^{2} = \frac{9}{4} - 2 \\ \\ \rightarrow (\alpha - \beta ) {}^{2} = \frac{9 - 8}{4} \\ \\ \rightarrow (\alpha - \beta ) {}^{2} = \frac{1}{4} \\ \\ \rightarrow \alpha - \beta = \sqrt{ \frac{1}{4} } \\ \\ \boxed{ \bf \rightarrow \alpha - \beta = \pm \frac{1}{2}}$

Answer 2

Answer:

Step-by-step explanation:

Sum of zeros =3/2

Product=-6

Now,

Alpha -ẞ²=alpha +ß²-4alpha ß

=3/2²-4×1/2

=9-8/4

=√1/4

=1/2.

Hope it will help you