if (2^3)^m = 16x30+2x6 find m
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Page No 2.33:
Question 1:
Find the zeros of each of the following quadratic polynomial and verify the relationship between the zeros and their coefficients:
(i) f(x) = x2 − 2x − 8
(ii) g(s) = 4s2 − 4s + 1
(iii) h(t) = t2 − 15
(iv) 6x2 − 3 − 7x
(v) p(x)=x2+22–√x−6
(vi) q(x)=3–√x2+10x+73–√
(vii)f(x)=x2−(3–√+1) x+3–√
(viii) g(x) = a(x2 + 1) − x(a2 + 1)
(ix) h(s)=2s2−(1+22–√)s+2–√
(x) f(v)=v2+43–√v−15
(xi) p(y)=y2+35√2y−5
(xii) q(y)=7y2−113y−23
ANSWER:
(i) We have,
f(x) = x2 − 2x − 8
f(x) = x2 + 2x − 4x − 8
f(x) = x (x + 2) − 4(x + 2)
f(x) = (x + 2) (x − 4)
The zeros of f(x) are given by
f(x) = 0
x2 − 2x − 8 = 0
(x + 2) (x − 4) = 0
x + 2 = 0
x = −2
Or
x − 4 = 0
x = 4
Thus, the zeros of f(x) = x2 − 2x − 8 are α = −2 and β = 4
Now,
and
Therefore, sum of the zeros =
Product of the zeros
= − 2 × 4
= −8
and