Tiêu đề GMAT-Formula Sheet Explanations.pdf ✅

FORMULA SHEET GMAT FOCUS Jamboree Education Pvt. Ltd. a is directly proportional to b: a ∝ b This implies that when a increases, b also increases and when a decreases, b also decreases. We can remove the proportionality sign by introducing a constant, say K. i.e. a = K b ⇒ a b = K Hence, the ratio will be constant. a is inversely proportional to b a ∝ 1 b This implies, when a decreases, b increases and when a increases, b decreases. We can remove the proportionality sign by introducing a constant, say K. i.e. a = K ( 1 b ) ⇒ ab = K Hence, the product will be constant. 6. ax2 + bx + c = 0 We know that (i) Roots of equation = Solution of equation When we solve a quadratic equation, we get two possible values of x, x1 and x2 respectively, which can be calculated with the quadratic formula as follows; x = −b ± √b 2 − 4ac 2a (ii) Sum of roots = x1 + x2 = −b a (iii) Product of roots = x1 x2 = c a 7.Roots of equation, Ax 2 + Bx + C = 0, are x = −B ± √B2 − 4AC 2A If B 2 – 4AC > 0 ⇒ 2 real roots B 2 – 4AC = 0 ⇒ 1 real root B 2 – 4AC < 0 ⇒ No real roots Hence, x 2 – 4x + 4 = 0 ⇒ B 2 – 4AC = 0 ⇒ 1 real root