Question

If the sum of zero is -1 and product is 7. Find it's quadratic polynomial

Answer 1

Answer

• The polynomial will be x²+x+7

Explanation

Given

• Sum of the zeros = -1
• Product of the zeros = 7

To Find

• The quadratic polynomial

Solution

So here if we assume α & β as the zeros of the polynomial

• α+β = -1
• αβ = 7

So then the polynomial will be given by,

• x²-(α+β)x+αβ

Sibstituting the given values,

→ x²-[(-1)]x + 7

→ x²+(1)(x) + 7

→ x²+x+7

Verification

→ α+β = -b/a

→ -1 = -1/1

→ -1 = -1

→ αβ = c/a

→ 7 = 7/1

→ 7 = 7

Where

• a = 1
• b = 1
• c = 7

Answer 2

$\bigstar \sf \bf\underline{ \underline{Given :-}}$

• Sum of zeroes = -1.
• Product of zeroes =7.

$\bigstar \sf \bf \underline{ \underline{To \: find:-}}$

• The quadratic polynomial.

$\bigstar \sf \bf\underline{ \underline{Solution:-}}$

We Know :-

If ax^2 + bx +c is a quadrilateral & its zeroes are p,q :

❥︎ p+q = - b/a

❥︎ pq = c/a

And if the sum of zeroes & product of zeroes are given , We find the quadratic polynomial through this eqn :

$\bigstar \underline{ \orange{\boxed{ \sf \: x^2 - (p+q)x+p}}}$

Acc to question :

➪ p + q = -1

➪ pq = 7

Therefore,

$\implies \sf {x}^{2} - ( - 1)x + 7 \\ \\ \implies \sf \: {x}^{2} + 1(x) + 7 \\ \\ \implies \sf \: \underline{ \underline{\orange{{x }^{2} + x + 7.}}}$

$\bigstar \sf \bf\underline{ \underline{Verification :- }}$

Here,

» a = 1

» b = 1

» c = 7

➪ p + q = -b/a

» -1 = - 1/1

» -1 = -1

» 1 = 1

➪ pq = c/a

» 7 = 7/1

» 7 = 7

» 1 = 1

Hence Verified !

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