Nature of roots & quadratic formula class 10 term-2 mathematics cbse board

Most important question class 10 chapter 4 Quadratic equation

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: (i) 2x^2-3x+5=0 (ii) 3x^2-4sqrt(3)x+4=0 (iii) 2x^2-6x+3=0

Write whether the following statements are true or false. Justify your answers. (i) Every quadratic equation has exactly one root. (ii) Every quadratic equation has atleast one real root. (ii) Every quadratic equation has atleast two roots. (iv) Every quadratic equations atmost two roots. (v) If he coefficient of x^(2) and the constnat term of a quadratic equation have opposite sigh, then the quadratic equation has real roots. (vi) If the coefficient of x^(2) and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.

in a class of 35 students , 17 have taken Mathematics , 10 have taken mathematics but not economics if each student has taken erither mathematics Of Economics or both , then the number of students who have taken Economics but not mathematics is

Find the roots of the following quadratic equations by the factorisation method. 3x^(2)+5sqrt(5)x-10=0

The roots of the quadratic equation 2x^2 - x - 6 = 0 are

If alpha, beta are the roots of the quadratic equation ax^(2)+bx+c=0, form a quadratic equation whose roots are alpha^(2)+beta^(2) and alpha^(-2) + beta^(-2) .

If 1 is a root of the quadratic equation 3x^2+a x-2=0 and the quadratic equation a(x^2+6x)-b=0 has equal roots, find the value of bdot