Question

If alpha and beta are the zeroes of polynomial 4x2+3x+7, find value of alpha square+beta square

Answer 1

4x² + 3x + 7

a and ß are the zeroes of the polynomial.

$\mathfrak\red{sum\:of\:the\:zeroes}$

• - cofficient of x / cofficient of x²
• -3/4

$\mathfrak\green{product\:of\:the\:zeroes}$

• constant term / cofficient of x²
• 7/4

$\huge\mathfrak\pink{solution\::-}$

• a² + ß²
• (a+ß)²=a²+ß²+2aß
• a² + ß² = (a+ß)² - 2aß
• (a+ß)² - 2aß
• (-3/4)² - 2(7/4)
• 9/16 - 14/4
• 9 - 56 /16
• $\fcolorbox{red}{green}{-47/16}$

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