Question

form a quadratic equation whose solution set is {-3,-2/5}. and the formula​

Answer 1

Step-by-step explanation:

Set of solutions/zeroes is { -3 , - 2/5}

Since, quadratic equation is given by:

p(x) = x² - {sum of zeroes} + {product of zeroes} ----------------(1)

Since,

Zeroes are - 3 and - 2/5.

Therefore,

Sum of zeroes = - 3 - 2/5

= (- 15 - 2)/5

= - 17/5 --------------(2)

Products of zeroes = (- 3)(- 2/5)

= 6/5 -------------(3)

Put (2) and (3) in (1):

p(x) = x² - { - 17/5 } + { 6/5 }

p(x) = x² + 17/5 + 6/5

Multiply above equation by 5:

p(x) = 5x² + 17x + 6

Therefore the required polynomial/quadratic equation is 5x² + 17x + 6

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