Quadratic equations CLASS 10 CBSE EX 4.2 Q1(1,2)

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

Statement -1 : A root of the equation (2^(10)-3)x^(2)-2^(11)x +2^(10)+3 =0 " is " 1 and Statement-2 : The sum of the coefficients of a quadratic equation is zero, then 1 is a root of the equation.

If alpha and beta are the roots of the quadratic equation x^(2) + px + q = 0 , then form the quadratic equation whose roots are alpha + (1)/(beta), beta + (1)/(alpha)

If p,q are roots of the quadratic equation x^(2)-10rx -11s =0 and r,s are roots of x^(2)-10px -11q=0 then find the value of p+q +r+s.

If a in (-1,1), then roots of the quadratic equation (a-1)x^2+a x+sqrt(1-a^2)=0 are

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0a n dalpha^2,beta is the roots of quadratic equation x^2-q x+8=0 , then the value of rifr/8 is the arithmetic mean of p a n d q , is

If p and q are roots of the quadratic equation x^(2) + mx + m^(2) + a = 0 , then the value of p^(2) + q^(2) + pq , is

The value of 'a' for which the quadratic equation 2x^(2) - x(a^(2) + 8a -1) + a^(2) - 4a = 0 has roots with opposite signs, lie in the interval

Consider the quadratic equation (log_10 8)x^2-(log_10 5)x=2(log_2 10)^-1 -x. Which of the following quantities are irrational.

Solve the following quadratic equations by factorization: 1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6