Question

The sum and product of zeroes of a quadratic polynomial are respectively 1/4 and – 1 . Then the corresponding quadratic polynomial is​

Answer 1

Answer:

$\huge \mathfrak \red{Answer↘}$

Sum of the zeroes= 4/1

Product of the zeroes=−1

Then the quadratic polynomial=x

2

−(Sum of the zeroes)x+(Product of the zeroes)

x 2 −( 4/1 )x−1

or 4x 2 −x−4 is the required quadratic polynomial.

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Answer 2

Given data: The sum and product of zeroes of a quadratic polynomial are 1/4 and -1 respectively.

To Find: The corresponding quadratic polynomial.

Solution:

• The polynomial of second degree with one or more variables is called quadratic polynomial or quadratic function.
• The general form of quadratic function is, $f(x)=ax^{2} +bx+c, a\neq 0$
• The sum of the zeroes of polynomial is $\alpha +\beta =\frac{-b}{a} =\frac{coefficient of x}{coefficient of x^{2} }$
• The product of the zeroes of polynomial is $\alpha .\beta =\frac{c}{a} =\frac{constant term}{coefficient of x^{2} }$
• The sum of the zeroes of polynomial is $\alpha +\beta =\frac{-b}{a} =\frac{-1/4}{1}$ , assume $a=1$
• The product of the zeroes of polynomial is $\alpha .\beta =\frac{c}{a}=\frac{-1}{1}$ , assume $a=1$
• The quadratic polynomial is of the form,
• $x^{2} -(\alpha +\beta )x+(\alpha .\beta )=0$
• Substitute, $\alpha +\beta =\frac{-1}{4},\alpha .\beta =-1$
• $x^{2} -(\frac{-1}{4} )x-(-1)=0$
• $x^{2} +\frac{1}{4}x+1=0$
• Multiply the equation by 4,
• $4x^{2} +x+4=0$
• Therefore, the corresponding quadratic polynomial is $4x^{2} +x+4=0$