Question

if the sum of squares of zeros of the polynomial 2xsquare +5x+k is 73/4find the value of k​

Answer 1

Step-By-Step Explanation:-

Let the two zeroes be a and b.

a² + b² = 73/4

Given polynomial is 2x² + 5x + k.

Sum of roots = - b/a

a + b = - 5/2

Product of roots = c/a

ab = k/2

(a + b)² - 2 ab = a² + b²

(-5/2)² -2×k/2 = 73/4

25/4 -k = 73/4

k = 25/4 - 73/4

k = 48/4

Answer 2

The data given in the question is sum of the squares of the zeroes of the polynomial is

$2 {x}^{2} + 5x + k \: is \: \frac{73}{4}$

we have to find the value of k.

sum of squares of zeroes is

${a}^{2} + {b}^{2} = \frac{73}{4}$

According to the equation sum of zeroes is -b/a

a+b=-b/a

=-5/2

product of zeroes is c/a

ab=c/a=k/2

${(a + b)}^{2} - 2ab = {a}^{2} + {b}^{2}$

${( \frac{ - 5}{2}) }^{2} - 2 \frac{k}{2} = \frac{73}{4}$

$\frac{25}{4} - k = \frac{73}{4}$

$\frac{25}{4} - \frac{73}{4} = k$

$k = \frac{ - 48}{4} = - 12$

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