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Hi. I need help with these questions.
See image for question.
Answer 16 and 17

Hi. I need help with these questions. See image for question. Answer 16 and 17-example-1
User Godlike
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Explanation:

16.................................................

Given

  • Equation ax² + bx + c = 0
  • One of the roots is twice the other

To find

  • Show that 2b² = 9ac

Solution

Let the roots be p and q

The sum and product of the roots:

  • p + q = -b/a
  • pq = c/a

The sum of the roots, considering p = 2q,

  • p + q = 2q + q = 3q

And

  • 3q = -b/a ⇒ q = -b/(3a)

The product of the roots, considering p = 2q:

  • pq = 2q(q) = 2q²

And

  • 2q² = c/a

Substitute q with -b/(3a)

  • 2(-b/(3a))² = c/a
  • 2b²/(9a²) = c/a
  • 2b² = 9a²(c/a)
  • 2b² = 9ac

=================================================

17. .................................................

Given

Quadratic equation

  • ax² = bx + c = 0, with equal roots

To find

  • Show that b² = 4ac

Solution

Equal roots means the discriminant is zero:

  • D = √b² - 4ac
  • √b² - 4ac = 0
  • b² - 4ac = 0
  • b² = 4ac
User Martin Ellis
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