Question

2x² - 5x + 7= 0 find the value of a and b from this classification​

Answer 1

The roots of the equation 2x² - 5x + 7= 0 are $\alpha =\frac{5+i\sqrt{31 } }{4}$  and $\beta =\frac{5-i\sqrt{31 } }{4}$

Explanation:

Given:

2x² - 5x + 7= 0

To find:

α and β

Formula:

$\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

Solution:

==> 2x² - 5x + 7= 0

==> a = coefficient of x²

==> b = coefficient of x

==> c = constant

==> a = 2

==> b =-5

==> c=7

==> Substitute the values in the formula

==> $\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

==> $\alpha =\frac{-(-5)+\sqrt{(-5)^{2}-4(2)(7) } }{2(2)}$

==> $\alpha =\frac{5+\sqrt{25-(8)(7) } }{4}$

==>$\alpha =\frac{5+\sqrt{25-56 } }{4}$

==> $\alpha =\frac{5+\sqrt{-31 } }{4}$

==> $\alpha =\frac{5+\sqrt{-1\times31 } }{4}$

==>$\alpha =\frac{5+\sqrt{i^{2} \times31 } }{4}$

==>$\alpha =\frac{5+i\sqrt{31 } }{4}$

==>$\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

==>$\beta =\frac{-(-5)-\sqrt{(-5)^{2}-4(2)(7) } }{2(2)}$

==> $\beta =\frac{5-\sqrt{25-(8)(7) } }{4}$

==>$\beta =\frac{5-\sqrt{25-56 } }{4}$

==> $\beta =\frac{5-\sqrt{-31 } }{4}$

==> $\alpha =\frac{5+\sqrt{-1\times31 } }{4}$

==>$\beta =\frac{5-\sqrt{i^{2} \times31 } }{4}$

==>$\beta =\frac{5-i\sqrt{31 } }{4}$

The roots of the equation 2x² - 5x + 7= 0 are $\alpha =\frac{5+i\sqrt{31 } }{4}$  and $\beta =\frac{5-i\sqrt{31 } }{4}$

Answer 2

Answer:

a is 2x power 2 b is 5x

Step-by-step explanation: