Question

Find a quadratic polynomial whose sum and product of zeroes are 4,1 respectively.

Answer 1

Answer:

Step-by-step explanation:

α+β=4

αβ=1

p(x)=k[$x^{2}$+(α+β)x+αβ]

     =k [$x^{2}$+4x+1]

therefore the required polynomial is $x^{2}$+4x+1 where k=1

Answer 2

GIVEN:

• Sum of Zeroes = 4
• Product of Zeroes = 1

TO FIND:

• What is the quadratic polynomial ?

SOLUTION:

Take

• $\rm{ \alpha = 4}$
• $\rm{ \beta = 1}$

FORMATION OF POLYNOMIAL:

$\large{\boxed{\bf{\star \: POLYNOMIAL = x^2 -sx + p \: \star}}}$

Where,

• s = sum of Zeroes
• p = Product of Zeroes

According to question:-

On putting the given values in the formula, we get

$\rm{\hookrightarrow x^2 -(4)x + 1 }$

$\bf{\hookrightarrow x^2 -4x + 1 }$

❝ Hence, the quadratic polynomial is x² –4x + 1 ❞

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