If x =2/3 and x =-3 are the roots of the equation ax2+7x+b=0, find the values of a and b.
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If not the roots of the equation x^2-(m+1)x+(m+4)=0 are negative ,then what is the interval for value of m?
x2 - (m+1)x + m + 4 = 0 If the equation has ral roots, then the discriminant must be positive: Let us verify: d = b2 - 4ac > 0 ==> (m+1)2 -...
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What are the possible values of resistances which one can obtain by using resistors of values 2Ω, 3Ω and 6Ω? Justify your answer.
The following combinations can be obtained: (i) The individual resistances: 2Ω,3Ω,6Ω (ii) All in series: 11Ω (iii) All in parallel: 11Ω (iv) Three different possible mixed grouping of resistors:4Ω,9/2Ω36/5Ω
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If the roots of the equation (a-b)x^2 + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c.
(a-b)x2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B2 – 4AC = 0 (b-c)2 – [4(a-b) (c - a)] = 0 b2-2bc + c2 – [4(ac-a2 –...
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If sinϴ and cosϴ roots of the quadratic equation ax2+bx+c=0,prove that a2-b2+2ac=0
Another approach, we have, sinq+cosq=-b/a...(i) and sinq*cosq=c/a...(ii) squaring (i), sin^2q+2sinq*cosq+cos^2q=(b^2)/(a^2) or, 1+2*(c/a)=(b/a)^2 or, a^2+2ac=b^2 Now, LHS=a^2-b^2+2ac =a^2+2ac-b^2=b^2-b^2=0=RHS
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If the roots of the equation.
(a-b)x2 + (b-c) x+ (c - a) = 0 T.P 2a = b + c B2 – 4AC = 0 (b-c)2 – [4(a-b) (c - a)] = 0 b2-2bc + c2 – [4(ac-a2 –...
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Product of real roots of the equation x^2 + | x | + 9 = 0
(c) : x2 + |x| + 9 = 0 => |x|2 + |x| + 9 = 0 => \ no real roots (D < 0)
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If p and q are the roots of the equation x^2 + px + q = 0, then
(a) : Given S = p + q = – p and product pq = q => q(p – 1) = 0 => q = 0, p = 1 Now If q =...
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If one root of the equation x^2 + px + 12 = 0 is 4, while the equation x^2 + px + q = 0 has equal roots, then the value of q is
(c) : As x2 + px + q = 0 has equal roots ∴ p2 = 4q and one root of x2 + px + 12 = 0 is 4. ∴...
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Differentiate between molality and molality values for a solution. What is the effect of change in temperature on molarity and molality values?
Molarity is the number of moles of solute dissolved in one litre of solution whereas molality is the number of moles of solute per kilogram of the solvent. Molarity decreases...
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If x = 2 & x = 0 are two roots of the polynomial f(x) = 2x^3 - 5x^2 + ax + b. Find the values of and b.
f(x) = 2(2)3 - 5(2)2 + a(2) + b = 0 ⇒ 16 - 20 + 2a + b = 0 ⇒ 2a + b = 4 ....(i) ⇒ f(0) = 2(0)3...
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