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 》
Answers
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:
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