Question

Find the sum and product of the roots of equation - 8x'2 -25=0​

Answer 1

Step-by-step explanation

mark as brainliest...

follow on........

Answer 2

Sum the roots $\frac{5i}{2\sqrt{2}}-\frac{5i}{2\sqrt{2}}=0$

Product of the roots $\frac{5i}{2\sqrt{2}}\times (-\frac{5i}{2\sqrt{2}})=\frac{25}{8}$

Step-by-step explanation:

Given quadratic equation is $-8x^2-25=0$

To find the sum and product of the roots of the given equation :

Since given equation is a quadratic so it has two roots

• $-8x^2-25=0$
• $-(8x^2+25)=0$
• $8x^2+25=0$

• $8x^2+25-25=0-25$
• $8x^2=-25$
• $x^2=-\frac{25}{8}$
• $x=\sqrt{-\frac{25}{8}}$
• $=\frac{\sqrt{25i^2}}{\sqrt{8}}$ where $i^2=-1$
• $x=\pm \frac{5i}{2\sqrt{2}}$

Therefore the roots are $x=\frac{5i}{2\sqrt{2}}$ and $x=-\frac{5i}{2\sqrt{2}}$

Now sum the roots $\frac{5i}{2\sqrt{2}}-\frac{5i}{2\sqrt{2}}=0$

Product of the roots $\frac{5i}{2\sqrt{2}}\times (-\frac{5i}{2\sqrt{2}})=-\frac{(5i)^2}{(2\sqrt{2})^2}$

$=-(\frac{-25}{8})$

$=\frac{25}{8}$

Product of the roots $\frac{5i}{2\sqrt{2}}\times (-\frac{5i}{2\sqrt{2}})=\frac{25}{8}$