Question

Construct a quadratic equation, in the form of ax² + bx + c = 0, whose roots are 1/2 and -5​

Answer 1

Answer:

ax² + bx + c= 0 -1

⇒ a{ x² + (b/a) x + c/a } = 0

⇒ { x² + (b/a) x + c/a } = 0 , as a≠0

⇒ { x² - (-b/a) x + c/a } = 0

⇒ { x² - (α+β) x + (α*β)} = 0 , where α & β are the roots of the quadratic equation ax² + bx + c= 0.

[ As proved in the previous page, α+β = -b/a, & α*β = c/a ]

Thus, the quadratic equation whose roots are α & β is given by -

x² - (α+β) x + (α*β) = 0

or, x² - (sum of roots) x + (product of roots) = 0

Step-by-step explanation:

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