Find the sum and product of zeroes of the quadratic polynomial 3x²-x-4​

2 thoughts on “Find the sum and product of zeroes of the quadratic polynomial 3x²-x-4​”

1. Answer :–

   • Sum of zeroes = 1/3

   • Product of zeroes = -4/3

   Given :–

   • 3x² – x – 4 is a quadratic polynomial.

   To Find :–

   • The sum and product of zeroes of the given quadratic polynomial .

   Step By Step Explanation :–

   Polynomial => 3x² – x – 4

   As we know ⤵

   [tex] \bigstar\boxed{ \underline{ \tt{ \pink{Sum \: of \: zeroes = \cfrac{ – b}{a} }}}}[/tex]

   [tex] \bigstar \boxed{ \underline{ \tt{ \purple{Product \: of \: zeroes = \cfrac{c}{a} }}}}[/tex]

   So let’s do it !!

   Sum of zeroes will be ⤵

   [tex] \sf\: Sum \: of \: zeroes = \cfrac{ – ( – 1)}{3} \implies \cfrac{1}{3} [/tex]

   Product of zeroes will be ⤵

   [tex] \sf \: Product \: of \: zeroes = \cfrac{ – 4}{3} [/tex]

   Therefore sum of zeroes => 1/3 and product of zeroes => -4/3

   __________________________

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2. Given

   Roots of quadratic polynomials are [tex]\frac{4}{3},-1[/tex]

   explanation:

   Since we have given that

   [tex]3x^2-x-4[/tex]

   First we will find the zeroes of the quadratic polynomial.

   We will use “Split the middle terms”:

   [tex]3x^2-x-4=0\\\\3x^2+3x-4x-4=0\\\\3x(x+1)-4(x+1)=0\\\\(3x-4)(x+1)=0\\\\x=\frac{4}{3},-1[/tex]

   Now,

   Let, [tex]\alpha =\frac{4}{3},\beta =-1[/tex]

   Now, we will verify the relationship between the zeroes and coefficient.

   Sum of zeroes is given by

   [tex]\alpha +\beta =\frac{4}{3}-1=\frac{1}{3}\\\\\alpha \beta =-1\times \frac{4}{3}=\frac{-4}{3}\\and\\\\\alpha +\beta =\frac{-b}{a}=\frac{1}{3},\alpha\beta =\frac{c}{a}=\frac{-4}{3}[/tex]

   Hence, verified.

   Roots of quadratic polynomials are [tex]\frac{4}{3},-1[/tex]

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