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Download Chapter - Quadratic Equation and more Summaries Mathematics in PDF only on Docsity!
Quadratic Equations yearning Objectives atthe course of this chapter, you will be able to: g-4. Learn to solve quadratic equations by Com- pleting the Square 3-2 Learn to find real solutions from imaginary solutions on a graph ————— ae a 8-3. Understand the solutions of quadratic inequalities Afunction {defined by f(x) Saxta, x! + taxtay, mhere d,, 4), 25, -... 4, © R is called n degree polynomial while coefficient (a4, #0, € HV) is real. Ifa,, 4, Oy 50, € C, then it is called complex coefficient polynomial. Quadratic Polynomial Apolynomial of degree two in one variable f(x) = y = ax? + br+c, wherea#Oanda,b,ce R a leading coefficient, c —> absolute term / constant term lfa=0 then y = bx + ¢ S linear polynomial b #0 Ifa=0,c=0 then y = bx — odd linear polynomial 1. The solution of the quadratic equation, ax? + bx + ¢ -b+ Vb? -4ac rboEve ~aae 2a 4 #4 ae = Dis called the discriminant of the quadratic equation. = 0 is given by x = . The expression 2. Ifa@ and f are the roots of the quadratic equation ax? + bx +c=0, then; @arp=-= — wyap== Nature of Roots (1) Consider the quadratic equation ax? + bx + c = 0 where a,b,ce Randa<0 then; (a) D> 0 © roots are real and distinct (unequal) (b) D=0 © roots are real and coincident (equal) (c) D<0 © roots are imaginary (d) Ifp + ig is one root of a quadratic equation, then the other must be the conjugate p — ig and vice versa. (p,q ¢ Randi=V-1) (2) Consider the quadratic equation ax? + bx +c = 0 where a,b,c € Qanda¥0 then; (a) If D > 0 and is a perfect square, then roots are rational and unequal. (b) Ifa =p + fq is one root in this case, (where p is rational and V¢ is a surd) then the other root must be the conjugate of it i.e., 8 = p— V@ and vice versa, 
