Question

if (2^3)^m = 16x30+2x6 find m

Answer 1

Answer:

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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