If a,b,c,`in` R, find the number of real root of the equation `|{:(x,c,-b),(-c,x,a),(b,-a,x):}|`=0

The number of real roots of the equation |x|^(2) -3|x| + 2 = 0 , is

If f(x) =a+bx+cx^(2) and alpha,beta "and" gamma are the roots of the equation x^(3)=1 , then |{:(a,b,c),(b,c,a),(c,a,b):}| is equal to

Let a,b,c,d be distinct real numbers and a and b are the roots of the quadratic equation x^2-2cx-5d=0 . If c and d are the roots of the quadratic equation x^2-2ax-5b=0 then find the numerical value of a+b+c+d

If a, b, c are real and a!=b , then the roots ofthe equation, 2(a-b)x^2-11(a + b + c) x-3(a-b) = 0 are :

Let alpha,beta,gamma be the roots of (x-a) (x-b) (x-c) = d, d != 0 , then the roots of the equation (x-alpha)(x-beta)(x-gamma) + d =0 are :

Let a, b, c, p, q be the real numbers. Suppose alpha,beta are the roots of the equation x^2+2px+ q=0 . and alpha,1/beta are the roots of the equation ax^2+2 bx+ c=0 , where beta !in {-1,0,1} . Statement I (p^2-q) (b^2-ac)>=0 Statement 2 b != pa or c != qa .

If a+b+c=0 and a,b,c are ratiional. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.

If a ,b ,c ,d are four consecutive terms of an increasing A.P., then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b. real and equal c. integers d. real and distinct

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alpha and beta .