Question

If a, B are the zeroes of the polynomial 2x²-5x+7, form a quadratic polynomial whose zeroes are 3a and 3B.
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Answer 1

Answer:

2x² + 15x - 63 = 0

Step-by-step explanation:

Given Equation

⇒2x² +5x - 7 = 0

To Find

⇒α and β

⇒Form a Quadratic equation whose zeroes 3α + 3β

Now Take

⇒2x² +5x - 7 = 0

Use Middle term Splitting

⇒2x² +7x - 2x - 7 = 0

⇒x(2x +7) -1(2x + 7)= 0

⇒(x - 1) = 0 and 2x + 7 = 0

⇒x = 1 and 2x = -7

⇒x = 1 and x = -7/2

We get

⇒α = 1 and β = -7/2

Then

⇒3α = 3 and 3β = -21/2

General Equation

⇒x² - (sum of zeroes)x + Product of zeroes = 0

Now we get

⇒x² - (3-21/2)x + 3×-21/2 = 0

⇒x² - {(6-21)/2}x - 63/2 = 0

⇒x² + (15/2)x - 63/2 = 0

Taking Lcm

⇒2x² + 15x - 63 = 0

Answer

⇒Equation is 2x² + 15x - 63 = 0

hope it helps u....

Answer 2

Step-by-step explanation:

if alpha and beta are the zeroes of the quadratic polynomial f(x) = 2x^2 - 5x + 7 find a polynomial where zeroes are 2alpha + 3beta and 3alpha + 2beta