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Sia ? 6 years, 6 months ago
Let, the two zeroes of the polynomial f(x) = 4x2 - 8kx - 9 be α and -α.
Comparing f(x) = 4x2 - 8kx - 9 with ax2+bx+c we get
a = 4; b = -8k and c = -9.
Sum of the zeroes = α + (-α) ={tex}-\frac ba=\;-\frac{-8k}4 {/tex}
0 = 2k
k = 0
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Sia ? 6 years, 6 months ago
Given: ΔABC in which ∠B = 90°

Circle with diameter AB intersect the hypotenuse AC at P.
A tangent SPQ at P is drawn to meet BC at Q.
To prove: Q is mid point of BC.
Construction: Join PB.
Proof: SPQ is tangent and AP is chord at contact point P.
Therefore,∠2 = ∠3 [ since Angles in alternate segment of circle are equal]
∠2 = ∠1 [Vertically opposite angles]
∠3 = ∠1 …(i) [From above two relations]
∠ABC = 90° [Given]
OB is radius , therefore BC will be tangent at B.
Therefore,∠3 = 90° - ∠4 …(ii)
∠APB = 90° [∠ in a semi circle]
⇒ ∠C = 90° - ∠4....(iii)
From (ii) and (iii), ∠C = ∠3
Using (i), ∠C = ∠1
⇒ CQ = QP …(iv) [Sides opp. to = ∠s in ΔQPC]
∠4 = 90° - ∠3 [From fig.]
∠5 = 90° - ∠1
∠3 = ∠1
Therefore,∠4 = ∠5
⇒ PQ = BQ …(v) [Sides opp. to equal angles in ΔQPB]
From (iv) and (v),
BQ = CQ
Therefore, Q is mid-point of BC. Hence, proved.
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Ram Kushwah 6 years, 10 months ago
{tex}\begin{array}{l}21^{\mathrm n}=3^{\mathrm n\;}\times7^{\mathrm n}\\\mathrm{Now}\;3^{\mathrm n\;}\;\mathrm{and}\;7^{\mathrm n\;}\;\mathrm{are}\;\mathrm{always}\;\mathrm{odd}\;\mathrm{for}\;\mathrm{all}\;\mathrm{values}\;\mathrm{of}\;\mathrm n\\\mathrm{odd}\;\times\;\mathrm{odd}\;=\mathrm{odd}\\\mathrm{Hence}\;\;3^{\mathrm n\;}\times7^{\mathrm n}\;\mathrm{can}\;\mathrm{not}\;\mathrm{end}\;\mathrm{with}\;2,4,6,8\end{array}{/tex}
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Gaurav Seth 6 years, 10 months ago
the general form of every positive odd integer in terms of some integer p is 2p-1 where p>0
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