DOC-20230724-WA0004.
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JeodDZ. Quadratic equations. Quadratic equations.
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❖Quadratic equation (a + b) = a2 + b2 + 2(a)(b) (a+b)3 = a3 + 3a2b + 3ab3 + b3.
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. The standard form of quadratic. equation is :.
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. FOR EXAMPLE. (x + 1)2 = 2(x – 3). ➢ ( x )2 + ( 1 )2 + 2(x)(1) = 2x – 6 ➢ x2 + 1 + 2x = 2x – 6 ➢ x2 + 1 + 2x – 2x + 6 = 0 ➢ x2 + 7 = 0.
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. (x+ 2 ) 3 = 2x(x2-1). ➢ (x)3 + 3(x)2(2) + 3(x)(2)2 + (2)3 = 2x3 – 2x ➢ x3 + 6x2 + 12x + 8 = 2x3 – 2x ➢ 2x3 – 2x - x3 - 6x2 - 12x - 8 = 0 ➢ X3 -6x2 – 14x – 8 = 0.
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. middle term splitting =. factorisation. zeroes of the quadratic equation.
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. 100x2 – 20x + 1 = 0. ➢ 100x2 - 10x – 10 x + 1 = 0 ➢ 10x(10x – 1 ) – 1 ( 10x – 1) ➢ (10x -1) (10x -1).
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. Discriminant formula. Nature of roots. D = b2 – 4ac.
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. Formula D = B2 – 4ac. ❖A = 2 , B = 2 , C = 3 ❖(2)2 – 4(2)(3) = 0 ❖4 – 24 ❖-20 ❖D <0.
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. Solution of the root. X2- 3x – 4 = 0. First we solve D (b2 – 4ac).
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. 1. Which of the following is not a quadratic equation.
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. 4) IF D > 0 then what will be the nature of the root A) No real root B) real and distinct C) Two equal roots D) both B) and C) 5) The quadratic equation 3x2 – 5x + 2 = 0 has : A) D > 0 B) D < 0 C) D = 0 D) D ≠ 0 6) IF the zeroes of the quadratic polynomial p(x) = ax2 + bx + c = 0, a ≠ 0 are 4 , -5 then the roots of the quadratic equation are :.
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. 7) If the product of two consecutive odd positive integers is 323 , then the integers are A) 21,13 B) 19,17 C) 31,33 D) 29,27 8) IF the discriminant of the quadratic equation = ax2 + bx + c = 0 is zero then the roots of the equation : A) are rational and equal B) are irrational and equal C) Are real and equal D) do not exit in real.
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. 1.C) 5. A 2.D) 6.. A. 3.B) 7.. B. 4. B 8.. ANSWERS.
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. 1. DETERMINE THE VALUE OF K IN THE QUADRATIC EQUATION 4X2 – 3KX + 1 = 0 HAS EQUAL ROOTS.
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. 1.K = ± 4/3 2.X = 2/3 3.P = 4 4.X = 2 5.YESS. ANSWERS.
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. RAJ AND AJAY GO TO HIMACHAL BY THEIR OWN CARS. RAJ’S CAR TRAVELS AT A SPEED OF X WHILE AJAY’S CAR TRAVELS 5 KM/H FASTER THAN RAJ’S CAR. RAJ TOOK 4 HOURS MORE THAN AJAY TO COMPLETE THE JOURNEY OF 400 KM..
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. 2)Which of the following quadratic equation describe the speed of raj‘s car? A) X2 – 5X –5OO = 0 B) X2 + 4X – 400 = 0 C) X2 + 5X – 500 = 0 D) X2 – 4X + 400 = 0.
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. 1.A 2(X+5)KM 2.C – X2 + 5X – 500 = 0 3.A - 20 4.D - 16.