Quadratic Equations Notes For Class 10 Chapter 4 Download PDF
The polynomial of degree two is called quadratic polynomial and equation corresponding to a quadratic polynomial P(x) is called a quadratic equation in variable x.
Thus, P(x) = ax2 + bx + c =0, a â‰ 0, a, b, c âˆˆ R is known as the standard form of quadratic equation.
There are two types of quadratic equation.
(i) Complete quadratic equation : The equation ax2 + bx + c 0 where a â‰ 0, b â‰ 0,c â‰ 0
(ii) Pure quadratic equation : An equation in the form of ax2 = 0, a â‰ 0, b = 0, c = 0
The value of x for which the polynomial becomes zero is called zero of a polynomial For instance, 1 is zero of the polynomial x2 â€” 2x + 1 because it become zero at x = 1.
A real number x is called a root of the quadratic equation ax2 + bx + c =0, a 0 if aÎ±2 + bÎ± + c =0.In this case, we say x = Î± is a solution of the quadratic equation.
1. The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.
2. Roots of quadratic equation ax2 + bx + c =0 can be found by factorizing it into two linear factors and equating each factor to zero.
By adding and subtracting a suitable constant, we club the x2 and x terms in the quadratic equation so that they become complete square, and solve for x.
In fact, we can convert any quadratic equation to the form (x + a)2 â€” b2 = 0 and then we can easily find its roots.
The expression b2 â€” 4ac is called the discriminant of the quadratic equation.
Let quadratic equation is ax2 + bx + c = 0
Find D = b2 â€” M4ac.
(i) If D > 0, roots are given by x = -b + âˆšD / 2a , -b â€“ âˆšD / 2a
(ii) If D = 0 equation has equal roots and root is given by x = -b / 2a.
(iii) If D < 0, equation has no real roots.
Let the quadratic equation be ax2 + bx + c = 0 (a â‰ 0).
Thus, if b2 â€” 4ac â‰¥ 0, then the roots of the quadratic â€”b Â± âˆšb2 â€” 4ac / 2a equation are given by
â€”b Â± âˆšb2 â€” 4ac / 2a is known as the quadratic formula which is useful for finding the roots of a quadratic equation.
(i) If b2 â€” 4ac > 0, then the roots are real and distinct.
(ii) If b2 â€” 4ac = 0, the roots are real and equal or coincident.
(iii) If b2 â€” 4ac <0, the roots are not real (imaginary roots)
If Î± and Î² are two roots of equation then the required quadratic equation can be formed as x2 â€” (Î± + Î²)x + Î±Î² =0
Let Î± and Î² be two roots of the quadratic equation (ax2 + bx + c = 0 then Sum of Roots: â€“ the coefficient of x / the coefficient t of x2 â‡’ Î± + Î² = â€“ b / a
Î±Î² = constant term / the coefficient t of x2 â‡’ Î±Î² = c / a
Translating the word problem into Mathematics form (symbolic form) according to the given condition
Step 2 :- Form the word problem into Quadratic equations and solve them.
Please send your queries to email@example.com you can aslo visit our facebook page to get quick help. Link of our facebook page is given in sidebar
Copyright @ ncerthelp.com A free educational website for CBSE, ICSE and UP board.