Question

if a zero of quadratic polynomial is 2+root 5 and Sum of zeroes is 4 find the quadratic polynomial

Answer 1

Hiii friend,

Let Alpha and beta are the zero of the polynomial.

Let Alpha = 2+✓5

Sum of zeroes = 4

Alpha + Beta = 4

2+✓5 + Beta = 4

Beta = 4-2-✓5

Beta = 2-✓5

Therefore,

Product of zeroes = (Alpha × Beta) = (2+✓5)(2-✓5) = (2)² - (✓5)² = 4-5 = -1

Therefore,

Required Quadratic polynomial= X²-(Alpha+Beta)X + Alpha × Beta

=> X²-(4)X + (-1)

=> X²-4X-1

HOPE IT WILL HELP YOU...... :-)

Answer 2

Solutions.

Let other zero be x

Then,
$2 + \sqrt{5} + x = 4 \\ = > \sqrt{5} + x = 2 \\ = > x = 2 - \sqrt{5} \\ now \: we \: have \: finded \: other \: zeroes = 2 - \sqrt{5} \\ so \: product \: of \: zroes \: = (2 + \sqrt{5)} (2 - \sqrt{5)} \\ = 4 - 5 \\ = - 1 \\ \\ now \: requird \:polynomial \\ {x}^{2} (sum \: of \: zeroe)x + (product \: of \: zeroes) \\ \\ {x}^{2} + ( 4)x + ( - 1) \\ = {x}^{2} + 4x - 1 \\ is \: your \: required \: polynoial$
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hope it helps you☺