Question

If alpha and beta are the zeros of polynomial 6x2-7x-3,then form a quadratic polynomial whose zeros are 2alpha and 2 beta.
10class 《polynomials 》

Answer 1

Answer:

x^2 -7x -6 is the answer.

Step-by-step explanation:

6x^2 - 7x - 3 = 0

ax^2 + bx + c = 0

here;

a = 6

b = -7 and

c = -3

alfha + beta = -b/a = -(-7)/6 = 7/6

alfha × beta = c/a = -3/6 = -1/3

x^2 + (alpha + beta)x + alpha × beta

2 alpha + 2 beta = 2(alpha + beta) = 2×7/6 =7/3

2 alpha × 2 beta = 4 alpha × beta = 4×-1/2 = -2

x^2 -7/3x -2 = 0

x^2 +(-7x-6)/3 = 0

x^2 -7x -6 = 0×3

x^2 -7x -6 = 0

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Answer 2

Answer:

Step-by-step explanation:

6x^2 - 7x - 3 = 0

ax^2 + bx + c = 0

here;

a = 6

b = -7 and

c = -3

alfha + beta = -b/a = -(-7)/6 = 7/6

alfha × beta = c/a = -3/6 = -1/3

x^2 + (alpha + beta)x + alpha × beta

2 alpha + 2 beta = 2(alpha + beta) = 2×7/6 =7/3

2 alpha × 2 beta = 4 alpha × beta = 4×-1/2 = -2

x^2 -7/3x -2 = 0

x^2 +(-7x-6)/3 = 0

x^2 -7x -6 = 0×3

x^2 -7x -6 = 0