Find the zeros of the polynomial …
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Yogita Ingle 6 years, 9 months ago
X² + 7/2x + 3/4 = 0
⇒x² + 7/2x = -3/4
⇒x² + 7/2x + (7/4)² = -3/4 + (7/4)²
⇒ x² + 2.(7/4).x + (7/4)² = -3/4 + 49/16
⇒(x + 7/4)² = (-12 + 49)/16
⇒(x + 7/4)² = 37/16
Taking square root both sides,
⇒x + 7/4 = ± √37/4
⇒ x = -7/4 ± √37/4
Hence, roots are (-7 + √37)/4 and (-7 - √37)/4
Now , some of roots = -coefficient of x/Coefficient of x²
= -(7/2)/1 = -7/2
and { (-7 + √37) + (-7 - √37)}/4 = -7/2
Also product of roots = constant/Coefficient of x² = 3/4
And {-7+√37}{-7-√37}/16 = {7² - √37²}/16 = 12/16 = 3/4
You can see both sum of roots and products are verified above explanation.
1Thank You