Find quadratic polynomial whose sum of zero and products of zero hour respectively 4 and 1.​

Find quadratic polynomial whose sum of zero and products of zero hour respectively 4 and 1.​

1 thought on “Find quadratic polynomial whose sum of zero and products of zero hour respectively 4 and 1.​”

1. $$\large {\pmb{\mathfrak{\red{Given…}}}}$$

Given that, 4 and 1 are the sum and product of the zeroes of a polynomial respectively.

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$$\large {\pmb{\mathfrak{\red{To~ find…}}}}$$

We have to find the polynomial.

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$$\large {\pmb{\mathfrak{\red{Solution…}}}}$$

According to the question,

• Sum of zeroes = 4 = : $$\sf \alpha+\beta$$
• Product of zeroes = 1 : $$\sf \alpha\beta$$

We know that :

$$\underline{\pmb{\bf{\green{Polynomial= x^2-(Sum~of~ the ~ zeroes)x+(Product~of ~ the ~zeroes)}}}}$$

Now, from the question, we’ll substitute the sum and product of the zeroes in the formula above and form the polynomial :

$$:\implies \sf x^2-(\alpha+\beta)x+(\alpha\beta)$$

$$: \implies \sf {x}^{2} – (4)x + (1)$$

$$: \implies\sf {x}^{2} – 4x + 1$$

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$$\pmb{\bf{\green{\therefore~x^2-4x+1~is~the~required~polynomial.}}}$$

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$$\large {\pmb{\mathfrak{\red{Important~points…}}}}$$

• $$\sf \alpha+\beta+\gamma=\dfrac{-b}{a}$$
• $$\sf \alpha\beta\gamma=\dfrac{-d}{a}$$
• $$\sf \alpha\beta+\beta\gamma+\gamma\alpha=\dfrac{c}{a}$$
• Quadratic formula = $$\sf \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$