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The no. of points of intersection of the two curvesy=2 sinx and y=5x2+2x+3 is :

Khushi goyal , 7 Years ago
Grade 11
anser 1 Answers
Vikas TU

Last Activity: 7 Years ago

Dear Student,
5x^2 + 2x + 3 is a parabola (highest degree = 2) has critical points at x = -2/10 = - 0.2(as x = - b/(2a) for the vertex of the parabola)
now,y = ax² + bx + c:
It's a minimum because the coefficient of x² is +ve so graph is concave upwards.
value of y at this lowest point of the parabola is
5*(-0.2)^2 -0.4 + 3= 2.8
Now range of 2sin x is [-2, 2], Here the 2 functions can never have same value,the curves do not intersect.
So no. of points of intersection of the 2 curves =0.
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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