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Form a quadratic polynomial whose one zero is 6 and sum of the zeroes is 0.
4. Find the sum of all natural numbers less than

By Charlotte

Form a quadratic polynomial whose one zero is 6 and sum of the zeroes is 0.
4. Find the sum of all natural numbers less than 100 which are divisible by 6.
1
are yeroes of nolynomial
2x + (k 4). find the value of​

About the author
Charlotte

3
17. If tan
then
(1 + sin 0) (1 – sin 0)
(1 + cos 0) (1 – cos 0)
4​

x²-x-6
/
x²+x-12
x++4×3+3×2
+
x3+4x²​

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  1. SOLUTION

    TO DETERMINE

    1. Form a quadratic polynomial whose one zero is 6 and sum of the zeroes is 0.

    2. Find the sum of all natural numbers less than 100 which are divisible by 6.

    CONCEPT TO BE IMPLEMENTED

    If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

    [tex] \sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }[/tex]

    EVALUATION

    1. Here it is given that one zero is 6 and sum of the zeroes is 0.

    Then other zero = 0 – 6 = – 6

    Product of the Zeros

    = – 6 × 6

    = – 36

    Hence the required polynomial

    [tex] \sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }[/tex]

    [tex] \sf{ = {x}^{2} – 0.x + ( – 36)}[/tex]

    [tex] \sf{ = {x}^{2} – 36}[/tex]

    2. We have to find the sum of all natural numbers less than 100 which are divisible by 6.

    Now the natural numbers less than 100 which are divisible by 6 are 6 , 12 , 18 , 24, .., 96

    This is an arithmetic progression

    First term = a = 6

    Common Difference = d = 12 – 6 = 6

    Let there are n terms

    So by the given condition

    6 + 6(n-1) = 96

    [tex] \implies \sf{6(n – 1) = 90}[/tex]

    [tex] \implies \sf{(n – 1) = 15}[/tex]

    [tex] \implies \sf{n = 16}[/tex]

    Hence the required sum

    [tex] \displaystyle \sf{ = \frac{n}{2} \bigg( \: First \: term + Last \: term \bigg) }[/tex]

    [tex] \displaystyle \sf{ = \frac{16}{2} \bigg( \: 6 + 96\bigg) }[/tex]

    [tex] \displaystyle \sf{ = \frac{16}{2} \times 102 }[/tex]

    = 8 × 102

    = 816

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