Question

3 is one of the zero of a polynomial having the sum is 0.write the quadratic polynomia​

Answer 1

Answer:

Given : Sum of the zeroes (α + β) = 0 and one zero (α) = 3 . On substituting β = - 3 in eq 1 . Hence, the required quadratic polynomial is x² - 9.

Answer 2

Step-by-step explanation:

Given⤵

➡3 is one of the zero of a polynomial having the sum is 0.

To find⤵

➡Quadratic polynomial.

Solution⤵

$⚫ Let \:the\: \alpha \: is \: 3.\\⚫ We \:know \:that \:sum \:of\:zeros\: is \:zero. \\ \alpha+ \beta= 0 \:\:\: ... (i) \\⚫Putting\: \alpha = 3\: in\: equation \:(i),\:we\: get\\ 3+\beta= 0\\ \beta = 0-3\\ \beta =(-3)\\⚫Now\:using\: formula\\ x²-(\alpha+\beta)x+\alpha\beta \: ,we \: get\\➡x²-[3+(-3)]x+3×(-3)\\➡x²-0x-9\\➡x²-9 \\ ✅Hence , \: the \: polynomial\: is \: x²-9.$

✔Extra points⤵

✡If and is given and asking the

quadratic polynomial then we use formula that is

x²-(α+ β) x+αβ where α and β are zeros.

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